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2010 A Probabilistic and Graphical Analysis of Evidence in O.J. Simpson's Murder Case Using Bayesian Networks Kunle Olumide

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COLLEGE OF ARTS AND SCIENCES

A PROBABILISTIC AND GRAPHICAL ANALYSIS OF EVIDENCE IN

O.J. SIMPSON’S MURDER CASE USING BAYESIAN NETWORKS

KUNLE OLUMIDE

A Dissertation submitted to the Department of Statistics in partial fulﬁllment of the requirements for the degree of Ph.D.

Degree Awarded: Fall Semester, 2010 The members of the Committee approve the Dissertation of Kunle Olumide defended on October 14, 2010.

Fred Huﬀer Professor Directing Dissertation

Valerie Shute University Representative

Debajyoti Sinha Committee Member

Xufeng Niu Committee Member

Wayne Logan Committee Member

Approved:

Dan McGee, Chair Department of Statistics

Joseph Travis, Dean, College of Arts and Sciences

The Graduate School has veriﬁed and approved the above named committee members.

ii ACKNOWLEDGEMENTS

In the beginning of my research work, I knew I wanted to do something related to application of statistics in law but didn’t know exactly what to do. A sincere gratitude to Prof. Joseph Kadane of Carnegie Mellon University who first suggested my dissertation idea to me when I was without one. Next, I would like to express my profound gratitude to my major advisor, Dr. Huffer, for accepting the challenge of being my advisor in an area where neither one of us had any prior experience. I would also like to express my sincere thanks to him for his leadership, guidance, patience, and his religious attention to details. My gratitude also goes to Dr. Valerie Shute of FSU College of Education, a member of my dissertation committee and the University representative, for her comments, suggestions, and her attention to details. My dissertation is of the current quality, in part, because of her contributions. Thank you so much. A huge thanks to Prof. Wayne Logan of FSU College of Law - a committee member -for providing legal perspective and guidance to my dissertation. I would also like to express my appreciation to the rest of my committee members, Dr. Sinha and Dr. Niu. When I first came to the graduate program in Statistics at FSU, it was the early direction and support that I received from Dr. Niu that sustained me through the end of the program. He was always caring and showing that he wanted me to succeed. Dr. Niu, I’m proud of you and grateful for your assistance and friendship.

I cannot leave the department without thanking many of the faculty members who have been influential in one way or the other in my studies at the department. Thanks to you all. Sincere thanks to all of the staff in the department office under the leadership of Pam McGhee and also to James, our computer administrator. Last but not the least, I want to say thank you to all the great friends I made in the department; you have enriched my life in a very significant way. I appreciate you all.

iii — Kunle

iv TABLE OF CONTENTS

List of Tables ...... vii

List of Figures ...... viii

Abstract ...... ix

1. Introduction ...... 1

2. Probability basis for the analysis ...... 8 2.1 Probability Basis ...... 8 2.2 Subjective Probability ...... 9 2.3 Bayes’ Theorem ...... 9 2.4 Odds, Likelihood, and Likelihood Ratio ...... 10 2.5 Our Hypotheses, Evidence and Likelihood Ratios ...... 12

3. Bayesian Networks ...... 18 3.1 General Descriptions and Examples ...... 18 3.2 Conditional Independence ...... 25

4. Analysis ...... 31 4.1 Motives ...... 33 4.2 Opportunity to commit the murders ...... 39 4.3 The Gloves ...... 49 4.4 The weapon (knife) ...... 61 4.5 Knowledge of Guilt ...... 70 4.6 Blood Stains ...... 76 4.7 Sensitivity Analysis ...... 87 4.8 Combining the Stories ...... 89

5. Conclusion ...... 93 5.1 Conclusions and further work ...... 93

APPENDIX ...... 97

A. BRIEF DESCRIPTIONS OF THE EVIDENCE ITEMS ...... 97

REFERENCES ...... 113

v BIOGRAPHICAL SKETCH ...... 114

vi LIST OF TABLES

3.1 Prior probabilities for chest illness diagnosis network...... 23

3.2 Posterior probability values for Chest illness diagnosis...... 24

4.1 Prior probabilities for propositions relating to O.J. Simpson’s Motives for the murder. .. 37

4.2 Posterior probabilities for propositions relating to O.J. Simpson’s Motives for the murder. 38

4.3 Prior probabilities for propositions relating to O.J. Simpson’s Opportunity to commit the murders...... 46

4.4 Posterior probabilities for propositions relating to O.J. Simpson’s Opportunity to commit the murders...... 47

4.5 Prior probabilities for propositions relating to “The Gloves” evidence...... 58

4.6 Posterior probabilities for propositions relating to “The Gloves” evidence...... 59

4.7 Prior probabilities for propositions relating to “The Weapon” evidence...... 68

4.8 Posterior probabilities for propositions relating to “The Weapon” evidence...... 68

4.9 Prior probabilities for propositions relating to O.J. Simpson’s Knowledge of Guilt. .... 74

4.10 Posterior probabilities for propositions relating to O.J. Simpson’s Knowledge of Guilt. .. 74

4.11 Prior probabilities for propositions relating to Blood stains evidence...... 83

4.12 Posterior probabilities for propositions relating to Blood stains evidence...... 84

4.13 Likelihood ratios for “Motives”...... 88

4.14 Likelihood ratios for “Opportunity to commit the murders”...... 89

4.15 Aggregate likelihood ratios for “Motives” and “Opportunity to commit the murders”. .. 89

4.16 Aggregate likelihood ratio for all the evidence combined...... 91

vii LIST OF FIGURES

1.1 Schematic representation for the Probanda and Evidence sectors ...... 7 3.1 A simple Bayesian network ...... 20

3.2 A Bayesian Network for Chest Diagnosis ...... 22 3.3 A simple example (taken from [1]) ...... 27 4.1 A Bayesian Network for Motives ...... 38

4.2 A Bayesian network for Opportunity to commit the murders ...... 48 4.3 A Bayesian Network for “The Gloves” evidence ...... 60 4.4 A Bayesian Network for “The Weapon” evidence ...... 69

4.5 A Bayesian Network for Knowledge of Guilt ...... 75 4.6 Summary of DNA proﬁles in the Simpson case ...... 85 4.7 A Bayesian Network for Blood stains ...... 86

viii ABSTRACT

This research work is an attempt to illustrate the versatility and wide applications of the field of statistical science. Specifically, the research work involves the application of statistics in the field of law. The application will focus on the sub-fields of Evidence and Criminal law using one of the most celebrated cases in the history of American jurisprudence - the 1994 O.J. Simpson murder case in California. Our task here is to do a probabilistic and graphical analysis of the body of evidence in this case using Bayesian Networks. We will begin the analysis by first constructing our main hypothesis regarding the guilt or non-guilt of the accused; this main hypothesis will be supplemented by a series of ancillary hypotheses. Using graphs and probability concepts, we will be evaluating the probative force or strength of the evidence and how well the body of evidence at hand will prove our main hypothesis. We will employ Bayes rule, likelihoods and likelihood ratios to carry out such an evaluation. Some sensitivity analyses will be carried out by varying the degree of our prior beliefs or probabilities, and evaluating the effect of such variations on the likelihood ratios regarding our main hypothesis.

ix CHAPTER 1

Introduction

This research work is an attempt to illustrate the versatility and wide applications of the field of statistical science. Specifically, the research work involves the application of statistics in the field of law. The application will focus on the sub-fields of Evidence and Criminal law using one of the most celebrated cases in the history of American jurisprudence - the 1994 O.J. Simpson murder case in California. In this case, O.J. Simpson was charged with the murder of his ex-wife and another man, but was eventually found not guilty of the crime. Our task here is to do a probabilistic and graphical analysis of the body of evidence in this case using Bayesian Networks. We will begin the analysis by first constructing our main hypothesis regarding the guilt or non-guilt of the accused; this main hypothesis will be supplemented by a series of ancillary hypotheses. Using graphs and probability concepts, we will be evaluating the probative force or strength of the evidence and how well the body of evidence at hand will prove our main hypothesis. Our assessment in some cases will focus on individual items of evidence and in others will focus on collections of evidence items with the ultimate goal of determining the probative force of the entire body of evidence. Although there are other measures of probative force of evidence [2], we will employ Bayes theorem, likelihoods and likelihood ratios to carry out such measure. Some sensitivity analysis will be carried out by varying the degree of our prior beliefs or probabilities, and evaluating the effect of such variations on the likelihood ratios regarding our main hypothesis.

The motivation for this research came from the book titled: A Probabilistic Analysis of the Sacco and Vanzetti Evidence (1996) by Joseph Kadane and David Schum. This book was about the analysis of evidence in a well-known legal case in the 1920s where two members, Sacco and Vanzetti, of an anarchist group at the time were tried, convicted and executed

1 for robbery and murder in Boston, Massachussetts. In their analysis, Kadane and Schum employed Wigmore Charts, Bayesian Networks, and probability to tell several plausible probabilistic stories regarding the evidence in the Sacco and Vanzetti case. For that body of work, they constructed about twenty eight Wigmore charts and combined some (not all) of them to construct two Bayesian networks for the case, labelled “Firearms Evidence” and “Consciousness of Guilt Evidence.” Our analysis will follow in the same path, though without the use of Wigmore Charts. Wigmore charts are logical and qualitative representations of the structure of a legal argument without the use of probabilities. Bayesian networks are very similar to Wigmore charts with their nodes treated as random variables which lend the networks to probabilistic analysis. Since this is a research work in statistics, though applied in legal settings, we feel it is apt to focus on probabilistic analysis of our case. To this end, all of our networks are Bayesian networks and we constructed six of them in total for this case.

Evidential Anecdote

On the evening of June 12th 1994, Nicole Brown Simpson and Ronald L. Goldman were found dead, right in the courtyard of Nicole’s condo in Brentwood California. The two victims were brutally murdered, each with a slash of the throat and multiple stab wounds to other parts of the body. Shortly after, the ex-husband of Nicole, Orenthal James Simpson, was charged with ﬁrst degree murder in the killings of the two victims.

The Objective of this work is to conduct a probabilistic and graphical analysis of the body of evidence generated by this case. This body of evidence consists of Grand Jury, Preliminary Hearing, and Trial evidence, and also the book written by the man himself, O.J. Simpson. One word that will frequently appear in this writing is the word “Probandum” which was ﬁrst coined by John H. Wigmore (See Wigmore, The Science of Proof, 1937). It is commonly used in the literature on analysis of evidence and will be adopted throughout this analysis. It is a Latin word meaning “that which is to be proved;” the plural form is probanda. We will begin the analysis by ﬁrst constructing the “Ultimate Probandum” which will be followed by “Penultimate Probanda.” The ultimate probandum is what the prosecution needs to prove, beyond reasonable doubt, in order to secure the conviction of the accused. This will be

2 the focal point of our analysis; however, for ease of analysis, the ultimate probandum will be divided into its component parts collectively referred to as the Penultimate probanda. The Penultimate probanda are a constellation of subsidiary probanda, each of which needs to be proved in order to prove the ultimate probandum. In statistical terms, the ultimate probandum is the major hypothesis to be tested while the penultimate probanda are a set of secondary hypotheses each of which needs to be proved to prove the major hypothesis. Since the case was tried in California, the Ultimate Probandum (the major hypothesis) will be derived from the rule of law as imposed by the State of California. Under section 187(a) of the California penal code:

Murder is the unlawful killing of a human being or a fetus with malice aforethought.

Section 189 of the same penal code upgrades the murder to “First degree Murder” if it was premeditated.

Malice aforethought is the “intent to do harm” such as killing; an element required in criminal prosecution. This is in contradistinction to accidental killing such as accidental discharge of a loaded gun that results in death. The intent can be formed well in advance of the act or instantaneously with the act. Premeditation is the deliberate thought and careful planning to commit a crime well in advance of the crime in order to either increase the likelihood of success, or to evade detection or apprehension.

Combining the two sections of the penal code, the Ultimate Probandum is constructed as follows:

Orenthal James Simpson (OJS or OJ) was guilty of ﬁrst degree murder in the deaths of Nicole Brown Simpson (NBS) and Ronald L. Goldman (RLG) that took place on June 12th 1994 in Brentwood, California.

As indicated earlier, it was this Ultimate Probandum that the prosecution, in our case, needed to prove - beyond reasonable doubt - to secure the conviction of the accused. But

3 the key element in the ultimate probandum is “first degree murder,” the requirements of which are laid out in the California penal code. Using all the salient elements of first degree murder as defined in the penal code, the Penultimate Probanda are constructed as follows:

PP1: Both NBS and RLG died of multiple stab wounds they received on the night of June 12th 1994.

PP2: Both NBS and RLG died of an unlawful act.

PP3: The perpetrator of the acts that resulted in the deaths of both NBS and RLG acted with malice aforethought.

PP4: The killing of NBS was committed with premeditation.

PP5: It was OJS who inﬂicted those multiple stab wounds that took the lives of both NBS and RLG.

To prove the ultimate probandum, the prosecution would need to prove each of the five penultimate probanda beyond reasonable doubt. However, the first two are usually not in dispute: In our case, nobody disputed the fact that both Nicole Simpson and Ronald Goldman were dead; neither did anyone contest the fact that the two victims died as a result of an unlawful act. Given the severity of the injuries sustained by each of the two victims, it was apparent that both victims probably died from those injuries. Indeed, the prosecution witness, Dr. Irwin Golden, the Deputy Medical Examiner at the Los Angeles County Coroner’s office who conducted autopsies of the two victims, testified to the cause of death at both the Grand Jury proceedings and the Trial. He unequivocally stated that the causes of death of the two victims were the injuries they sustained from the attack of the evening of June 12th, 1994. The next two probanda, PP3 and PP4 concern the state of mind of the perpetrator, malice aforethought and premeditation, which the defense never addressed. Instead, the defense made PP5 its focal point and purported to show that it wasn’t O.J. Simpson who committed the murders. The defense presented evidence to prove this assertion and attacked the credibility of any evidence from the prosecution that purported to show otherwise. For the defense to address PP3 and PP4 would be tantamount to conceding PP5 - that it was O.J. Simpson who committed the crime. Since the defense only contested PP5, probanda PP3 and PP4 became moot in the trial. So, if the defense claimed that it

4 wasn’t its client who committed the crime, which is usually the case in criminal cases, it would not be necessary for the defense to put up any argument relating to the state of mind of the perpetrator as we have in PP3 and PP4. As a result, the only one of the penultimate probanda that is usually in dispute is PP5, the identity of the perpetrator. Therefore, to prove the Ultimate Probandum, the prosecutor needed to prove - beyond reasonable doubt - that it was OJS who inﬂicted the multiple stab wounds that killed both NBS and RLG. In light of this, our analysis will be devoted to marshaling the evidence to prove PP5. To this end, the entire body of evidence will be divided into the six categories below and several propositions pertaining to them will be constructed to prove PP5. Each body of evidence will be used to construct a Bayesian network.

1. Motives

2. Opportunity to commit the murder

3. The Gloves

4. The Weapon (knife)

5. Knowledge of guilt

6. Blood stains

Figure 1.1 gives a schematic representation of the relationship of probanda and evidence categories.

Evidence and Relevance In the O.J. Simpson case, an enormous mass of data was generated in the form of evidence. Is all of this really evidence? it would be if it has any relevance to proving or disproving the case against the accused. In other words, any information that is helpful either to the prosecution or the defense in a legal case will be deemed evidence; i.e., when it is relevant to hypotheses of interest. On this issue, the United States Federal Rule of Evidence, FRE-403, deﬁnes Relevant evidence as follows:

“Relevant evidence” means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more

5 probable or less probable than it would be without the evidence.

In our current analysis, when we refer to evidence, we mean relevant evidence - those that are of consequence to matters at hand. In this body of work, only the relevant evidence will be charted and included in our networks for analyses. This is not to say that our analysis will include all relevant evidence in this case - far from it. To start, the body of evidence from the defense witnesses is not included in this analysis; our analysis contains only the body of evidence from the prosecution side. Besides, in spite of our diligence, it is also very likely that many relevant evidence items favorable to the prosecution that we had intended to use have been inadvertently omitted given the sheer amount of evidence generated in this case.

In this introductory chapter, we have laid out our objective and motivation for this dissertation and the path and procedures to be employed in our analysis. In Chapter 2, we present the probability basis for our analysis, explaining some basic probability concepts. We have included this chapter in anticipation of the paper being accessible to a wider audience since the research is an interdisciplinary work. Chapter 3 introduces our major tool of analysis in this work - a Bayesian network. In Chapter 4, we present a detailed analysis of our case, constructing a Bayesian network from each of our six bodies of evidence and computing from each a likelihood ratio for PP5. Chapter 5 presents the conclusions reached in our analysis and discusses possible future work on the subject of this dissertation. At the end of this document, we have included an appendix which provides more detailed information on the testimonies and witnesses which were included in our Bayesian networks.

6 Figure 1.1: Schematic representation for the Probanda and Evidence sectors

OJS was guilty of first-degree murder in the deaths of NBS and RLG

NBS and RLG NBS and Perpetrator The killing of OJS died of RLG died of acted with NBS was committed multiple stab an unlawful malice committed with the two wounds act aforethought premeditation murders

Motives Opportunity Knowledge for to commit the The Gloves The weapon Blood stains of Guilt murder murders

7 CHAPTER 2

Probability basis for the analysis

This chapter provides information on some basic concepts in probability. Because this is an interdisciplinary research work, we include this background material on probability (which will be already known to statisticians) in the hopes that this document will then be accessible to a wider audience.

2.1 Probability Basis

In an experiment with several outcomes where each outcome is assumed to be equally likely, we calculate the probability of an event by counting the number of outcomes favorable to the event of interest and dividing that by the total number of outcomes. Another way we calculate probability is through a relative frequency approach: In this case, we repeat an experiment many times and count the frequency of an event of interest and divide that by the number of repetitions of the experiment. Both of these approaches involve processes that are either replicable or repetitive; however there are many other situations, such as we frequently encounter in law and sometimes in other walks of life, where probability calculations are required but the conditions are neither replicable nor repetitive. These situations may involve events that are singular, unique or too destructive and dangerous to be contemplated, let alone replicated. For example, there has not been a nuclear war in the past and no one is looking forward to it any time in the foreseeable future. Although we have had a singular experience of holocaust and that of nine-eleven, no one wants to replicate these events; neither does anyone want to test-run a nuclear war in order to calculate the probability of its future occurrence. In legal cases, the task of estimating the probability of an accused - with no past criminal record - committing a murder is extremely daunting to say the

8 least. For some events, the world cannot be played over and over again just for the purpose of probability determination. In all of these cases, we will rely on the concept of “Subjective Probability” to estimate the probability of their past, present or future occurrences provided it does not violate any of the axioms of probability, i.e., the sum of the probability of an event and the probability of the complement of that event is equal to one, etc.

2.2 Subjective Probability

Because some events similar to the above-mentioned rare and non-replicable events are frequently encountered in law, and since this research work is centered on the analysis of a legal case, subjective probabilities will be used for most of our analysis. A subjective probability is a numerical evaluation of personal belief in the occurrence of an event based on personal knowledge and known relevant background information about the event. A subjective probability, though based on background information, is not unique but peculiar to individuals making the determination, and therefore varies from one person to another. These subjective probability values are frequently updated in light of new information (or evidence in our case) using a well known concept in probability - that of Bayes’s Theorem or Rule. With this approach, we start with a hypothesis of interest, assess the probability of this hypothesis referred to as the “Prior probability” based on knowledge and background information we possess at the time. We will then incorporate newly acquired knowledge regarding this hypothesis and then update the prior probability in light of the new evidence. This updated probability in the face of new evidence is referred to as the “Posterior probability.”

2.3 Bayes’ Theorem

Given any two events A and B, Bayes’ theorem, in its simplest form, tells us how to calculate the probability of one event, say A, given the knowledge of the other event, B, written as P(A|B). This probability is expressed thus:

P(B|A)P(A) P(A|B)= (2.1) P(B|A)P(A)+ P(B|Ac)P(Ac)

9 In general, we indicate the complement of an event by placing a superscript such as “c” on the symbol representing that event. So, Ac here represents the complement of the event A, although this is not the only way by which we represent the complement of an event.

If we now suppose an hypothesis H and an item of evidence E, P(H) will be the prior probability, i.e., the unconditional probability that the hypothesis is true before any knowledge of the evidence. And P(H|E) is the posterior probability, which is the conditional probability that the hypothesis is true in light of the evidence. Using the deﬁnition of conditional probability, we can write: P(H ∩ E) P(H|E)= which implies P(H ∩ E)= P(H|E)P(E) (2.2) P(E) In a similar manner, we can write

P(H ∩ E)= P(E|H)P(H) (2.3)

Combining (2.2) and (2.3) above, P(E|H)P(H) P(H|E)= (2.4) P(E) Using the law of total probability,

P(E)= P(E|H)P(H)+ P(E|Hc)P(Hc) (2.5) therefore, P(E|H)P(H) P(H|E)= (2.6) P(E|H)P(H)+ P(E|Hc)P(Hc) So, (2.6) is Bayes’ theorem in terms of our contemplated hypothesis and our item of evidence E. Before any further discussion about Bayes’, we need to deﬁne other terms, namely Odds, Likelihood, and Likelihood Ratio.

2.4 Odds, Likelihood, and Likelihood Ratio

c O c P(A) P c P For any event A, we deﬁne the odds of A to A as (A : A )= P(Ac) , where (A )=1− (A). For our hypothesis H, the odds of H to its complement Hc is P(H) O(H : Hc)= (2.7) P(Hc)

10 This will be referred to as the prior odds. If we now incorporate our knowledge of the evidence E, we can deﬁne the posterior odds of H to Hc, given the evidence E as follows: P(H|E) O(H : Hc|E)= (2.8) P(Hc|E)

The likelihood of the evidence E under hypothesis H is denoted by ℓE deﬁned as:

ℓE = P(E|H). (2.9)

Applying Bayes’ theorem as stated in (2.6) above to the deﬁnition of posterior odds, then

We can see that the ﬁrst ratio in equation (2.10) is the prior odds of H to Hc before we received the item of evidence E while the second ratio contains two likelihoods P(E|H) and P(E|Hc). We will refer to this second ratio as the likelihood ratio for evidence E on c hypotheses H and H denoted as LE, i.e., P(E|H) L = (2.11) E P(E|Hc)

Hence, we can re-write (2.10) as :

c c O(H : H |E)= O(H : H )LE (2.12)

from which we can write LE in terms of odds ratios as: O(H : Hc|E) L = (2.13) E O(H : Hc)

We can see that (2.13) quantiﬁes the eﬀect or strength of evidence E on the two c hypotheses H and H . In other words, the likelihood ratio LE measures the change, if

11 any, from prior odds to posterior odds after taking into account the item of evidence E.

We should ﬁrst note that if LE = 1, then evidence E favors neither of the two hypotheses, meaning that E has no probative value with regards to either hypothesis. However, if c LE > 1, evidence E favors hypothesis H over H , i.e., by considering evidence E, the odds has increased in favor of H by an amount indicated by the size of LE. If LE < 1, evidence E favors hypothesis Hc over H; i.e, the odds has decreased from prior to posterior in light of the evidence by an amount indicated by the size of LE. The mathematician A. Turing appears to have been the ﬁrst one to relate LE to the force of evidence, see [3], pg. 36-38. According to Kadane and Schum, Turing also suggested that to grade the inferential force of evidence, we can use the logarithm of LE. That means, taking the log of (2.13) above, we have

c c log(LE) = log[O(H : H |E)] − log[O(H : H )]. (2.14)

2.5 Our Hypotheses, Evidence and Likelihood Ratios

In the above discussion regarding the likelihood ratio, we referred to a generic hypothesis H; we now examine the likelihood ratio in terms of our penultimate probandum, PP5. We recall that PP5 states that it was O.J. Simpson who committed the two murders. This becomes our main hypothesis of focus from here on and we shall denote this main hypothesis by H5. In terms of our hypothesis and an item of evidence E, P(E|H ) L = 5 E P c (E|H5) O(H : Hc|E) = 5 5 (2.15) O c (H5 : H5) This begs the following two questions:

c 1. Is evidence E more probable if H5 or H5 is true? Are we more likely to obtain evidence E if O.J. was the perpetrator of the two murders than if he was not?

2. How do we then obtain this likelihood?

Based on Bayes’ rule, if we can somehow determine the prior odds O(H : Hc) and the posterior odds O(H : Hc|E), we then divide the posterior odds by prior odds to obtain the probative value of evidence E. As indicated earlier, this case is one of the most celebrated

12 legal cases in the U.S. history from the standpoint of who is on trial and the amount of evidence involved. The case generated a mass of evidence; indeed an avalanche of evidence was generated. Our task is to assess the probative value, strength, or force of this entire body of evidence. How then is this to be achieved? One approach is a simplistic one: we supply prior odds for our hypothesis and also assign posterior odds for the same hypothesis in light of the entire mass of evidence taken as a whole, and divide the posterior odds by the prior odds to obtain the likelihood ratio. However, the likelihood ratio and the probative strength of the evidence so obtained will not reveal the insights that can be gained by the separate examination of various subsets of the mass of evidence and the consideration of the important evidential interactions that may be taking place between them (see [4], pg. 128). A more efficient approach would be the age-old concept of “divide and conquer.” Application of this strategy to complex inference tasks was first proposed by Ward Edward, 1962 (see [4], pg. 128). According to this strategy, we divide up the entire mass of evidence into smaller segments or subsets and assess the probative value of each segment separately and then combine all the various probative values to determine the overall strength of the entire mass of evidence. To execute this strategy here, our entire mass of evidence is grouped into different categories of evidence where each category is a collection of several pieces of evidence items. In order to be able to calculate the likelihood ratio for any piece of the evidence or joint occurrence of two or more of them given some hypotheses, we will conceive each of the evidence items as an event which can be either true or false (it either occurred or did not occur). To effectively continue our discussion here, it is appropriate to introduce some notations. Let

• E∗ be the event representing the entire body of evidence, where the entire body is divided into subcollections.

∗ th • Ej be the event representing the j subcollection of evidence, for j = 1, ..., m, and ∗ m ∗ E = ∩j=1Ej

th th • eij be the event representing the i item of evidence in the j subcollection; i =1, ..., nj ∗ nj ∗ and Ej = ∩i=1eij, with nj being the number of items in Ej

For convenience, we shall adopt the following notational equivalence in the case of joint occurrence of two or more events:

13 P(A ∩ B)= P(A, B)= P(AB)

The evidence pieces or a collection of them just described are mostly testimonies from various witnesses. As we all know, testimonies can be true or false; the fact that a witness presents a testimony under oath does not necessarily make it true. Therefore, to make this distinction clear, we adopt the convention of using a letter for an event and the same letter with an asterisk for the testimony of a witness regarding that event. For example:

Suppose:

A = {The accused was at the crime scene} A∗ = {A witness testiﬁes that he saw the accused at the crime scene}

Clearly, the veracity of A∗ depends on A: If the accused was actually at the crime scene, the testimony from the witness (A∗) will be a true testimony; however, if the accused was never at the crime scene, then A∗ becomes a false testimony. In our analysis, we would often be interested in probabilities such as P(A∗|A), the conditional probability of the witness providing this testimony given that the accused was actually at the crime scene, and P(A∗|Ac), the conditional probability of the witness providing this testimony given that the accused was never at the crime scene. P(A∗|A) is commonly referred to as the “hit” probability while P(A∗|Ac) is referred to as the “false positive” probability.

∗ Now, for the collection of evidence in each subset Ej , we can write a likelihood ratio of the form: P ∗ (Ej |H5) LE∗ = (2.16) j P ∗ c (Ej |H5)

The size of this likelihood ratio indicates the strength of the collection of evidence items in ∗ Ej in determining the truth or falsity of our probandum of interest, i.e., the probative value of the evidence in reference to the guilt or innocence of O.J. Simpson. This probative value is speciﬁc to the collection of evidence in this subset only and such a likelihood value can be determined for each subset of the entire body of evidence. How do we then combine all the

14 likelihood ratio values for all the various subsets of evidence? To answer this question, let’s ∗ suppose that there is only one item of evidence e1j in the subset Ej . From (2.11), we can write

P(e |H ) L = 1j 5 (2.17) e1j P c (e1j|H5)

c as the likelihood ratio of the evidence e1j given H5 and H5. Instead of one, suppose there ∗ are two items of evidence e1j and e2j in Ej ; we now want to determine the likelihood ratio c of these two items of evidence given H5 and H5. First we deﬁne Le2j |e1j , the conditional likelihood of e2j given e1j as:

P(e |H ∩ e ) L = 2j 5 1j , (2.18) e2j |e1j P c (e2j|H5 ∩ e1j) then

Le1j ∩e2j = Le1j Le2j |e1j (2.19)

where Le1j ∩e2j is the likelihood ratio for the evidence items e1j and e2j combined given c hypotheses H5 and H5. Referring back to (2.18), the question we should attempt to answer is:

c Does our assessment of the probability of e2j conditional on H5 (or H5) depend on our knowledge of e1j?

If the answer to this question is no, then evidence items e1j and e2j are said to be independent, c conditional on H5 (or H5). In this case, Le2j |e1j = Le2j which indicates that the probative value of the item of evidence e2j does not depend on the knowledge of e1j. If on the other hand, we answer that question in the aﬃrmative, that means that our assessment of the probability of e2j does depend on the knowledge of e1j and Le2j |e1j =6 Le2j . In this case, evidence items e1j and e2j are said to be conditionally nonindependent (dependent) under c either or both of H5 and H5 . This indicates that the probative value of e2j does depend on the knowledge of e1j.

15 ∗ If we now suppose we have n evidence items e1j, e2j,. . . ,enj in subset Ej , then we can generalize equation (2.18) above and deﬁne the likelihood ratio of evidence item eij given all the preceding i − 1 items as:

P(eij|H ,e i j,e i j,...,e j,e j) L = 5 ( −1) ( −2) 2 1 (2.20) eij |e(i−1)j ,e(i−2)j ,...,e2j ,e1j P c (eij|H5,e(i−1)j,e(i−2)j,...,e2j,e1j) Now, for this entire collection of n evidence items, the likelihood ratio of their joint occurrence can be written as:

Le1j ∩e2j ∩...∩enj = Le1j Le2j |e1j Le3j |e2j e1j ...Lenj |e(n−1)j ...e2j e1j (2.21)

∗ ∗ The preceding two equations pertain to all the evidence items in the subset Ej of E , the ∗ entire body of evidence. We can then calculate the likelihood ratio for each subset Ej keeping in mind that the evidence in any previously considered subset may aﬀect our judgment of ∗ Ej . Such a likelihood ratio will be of the form:

P ∗ ∗ ∗ ∗ ∗ (Ej |H5,Ej−1,Ej−2,...,E2 ,E1 ) LE∗|E∗ ,E∗ ,...E∗,E∗ = (2.22) j j−1 j−2 2 1 P ∗ c ∗ ∗ ∗ ∗ (Ej |H5,Ej−1,Ej−2,...,E2 ,E1 ) Finally, we can then obtain the aggregate likelihood ratio for the entire body of evidence as follows:

∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ LE1 ∩E2 ∩...∩Em = LE1 LE2 |E1 LE3 |E2 E1 ...LEm|Em−1...E2 E1 (2.23)

In formulating the likelihood ratio expressed by equation (2.20) above, we assume that each evidence item eij is directly linked by a single reasoning stage to our probanda of c interest H5 and H5. However, as we will see in chapter 4, there are often many links in a chain of reasoning connecting an item of evidence with the main hypothesis. In this case, the derivation of the likelihood ratio becomes more challenging, the likelihood ratio expression itself becomes more cumbersome, and the number of prior probabilities that would need to be speciﬁed increases. For example, consider again our hypothetical example of A and A∗ where:

16 A = {The accused was at the crime scene} A∗ = {A witness testiﬁes that he saw the accused at the crime scene}

∗ c c and now consider the following chain of reasoning: A −→ {A, A } −→ {H5, H5}; we recall that A∗ and A are not the same since A∗ is the evidence for event A. We know that just because a witness testiﬁes A∗ does not mean that event A is true. Here, we’ve been able to insert a reasoning stage between the evidence node A∗ and the probanda of interest c {H5, H5}. It can be shown that the likelihood ratio expression for the witness’ testimony, evidence node A∗ is (see [4], pg. 137 - 138):

∗ P(A |H5) L ∗ = A P ∗ c (A |H5) P(A|H )[P(A∗|AH ) − P(A∗|AcH )] + P(A∗|AcH ) = 5 5 5 5 (2.24) P c P ∗ c P ∗ c c P ∗ c c (A|H5)[ (A |AH5) − (A |A H5)] + (A |A H5) Given the likelihood ratio expression in equation (2.24) above with only one node between the evidence node and the probanda of interest, one can only imagine the complexity of the mathematics of the derivation of the likelihood ratio expression with several nodes between the evidence node and the probanda of interest. However, for our research, deriving many of the needed equations to carry out the analyses will not be necessary as there are many software systems available that have the capability of performing the analyses. Using any of these available systems, ﬁrst we construct the network and then supply the prior probabilities as required by the system. All the mathematics required to perform the analyses are buried inside the system and the system will select for the computer which equations are appropriate for the network constructed. For our analyses, we will employ the use of two of the available software packages - Hugin and GeNIe (to be discussed in the next chapter). Once the prior probabilities are assigned and conditioning on some selected nodes, the systems propagate probabilities throughout the network and calculate the posterior probabilities for the states of the rest of the nodes according to the Lauritzen and Spiegelhalter algorithm upon which they are based.

17 CHAPTER 3

Bayesian Networks

3.1 General Descriptions and Examples

In addition to the application of probability concepts involved in this research work, another major component of the analysis will be the construction of a graph or network, known as a Bayesian network. A Bayesian network is used to model a domain containing uncertainties of some sort. The graph of a Bayesian network is a directed acyclic graph consisting of sets of nodes connected by directed arcs (links). It is acyclic in the sense that there exists no directed path starting and ending at the same node. The nodes of a Bayesian network are drawn as circles or ovals while the links are arrow-headed line segments. These nodes represent events or random variables, whereas the arcs show influential relationships or dependencies among the nodes or variables. A typical network will show arcs going in and out of the nodes while the nodes have parent-child relationships among themselves. A node that has an arc coming in is referred to as a child while a node that has an arc going out to another node is considered a parent. With that being said, it is possible and indeed typical for a node to have one or more parents, depending on whether there are one or more arcs coming in. It is also possible for a parent to have several children by sending out several arcs to different nodes. The structure of a Bayesian network is a graphical, qualitative illustration of interactions or dependencies among the variables. Numerically, it also represents a quantitative relationship among the variables. A variable node can either be discrete with a finite number of states or continuous such as Gaussian, each with its own probability distribution. A node without any parent, i.e., no link pointing to it, is called a root node which is described by giving its marginal distribution, while a child-node with arcs coming in is described by a conditional probability distribution, conditioning on its immediate predecessors, i.e., those nodes from which it directly receives arcs.

18 3.1.1 Example 1

Figure 3.1 is a simple generic example of a Bayesian network. This basic network consists of ﬁve nodes, A, B, C, D, E connected by arcs or links. Each node represents a random variable. For the sake of simplicity here, we shall assume the variables are discrete random variables with ﬁnitely many states. Consistent with the discussion immediately preceding, nodes A and B are parents while D is a child, and so is E. Node C is both a parent and a child. C is the only parent of E but also a child of both A and B.

19 Figure 3.1: A simple Bayesian network

20 In Figure 3.1, we presented a very simple example of a Bayesian network; this general idea can be extended to many complicated situations. Once we have constructed the network, our main task is then to perform a probabilistic inference. In general, the computation of a probability of interest given a model is known as probabilistic inference (see [5]). For example, given a prior probability of a random variable being in a particular state, we may want to compute the posterior probability of the random variable being in that state in light of new evidence. To perform such probabilistic inference, many researchers have developed probabilistic inference algorithms for Bayesian networks with discrete variables that exploit the conditional independencies (to be discussed later). The most commonly used algorithm for discrete variables is the clustering algorithm ﬁrst proposed by Lauritzen and Spiegelhalter (1988), (see [5]) and later improved by Jensen et al. (1990), and Dawid (1992). The computational task of this research will be carried out using both the Hugin and GeNIe software. Hugin is a product of HUGIN EXPERT A/S, a software technology development company based in Denmark. GeNIe was developed by the University of Pittsburgh Decision Systems Laboratory. Although there are other algorithms available on both the Hugin and GeNIe packages, the default algorithm is the clustering algorithm which will be employed in our computations.

3.1.2 Example 2

Here is an example which applies a Bayes network to a real life problem involving a diagnosis of a patient’s chest illness. This example is from [6]. It is a simpliﬁed version of a Bayes net that could be used to diagnose patients arriving at a clinic. Figure 3.2 is a Bayes net constructed for the diagnosis.

21 Figure 3.2: A Bayesian Network for Chest Diagnosis

Visit to Smoker (S) Asia (A)

Has Has Lung Has Tuberculosis (T) Cancer © Bronchitis (B)

Tuberculosis or Lung Cancer (TOC)

Positive X- Shortness of ray (XR) Breadth (SB)

22 The network consists of eight nodes connected by links. Each node represents a condition of the patient; for example, “Smoker” represents whether the patient is a smoker or not. The links represent the relationships among the nodes, most of which are causations. The arrangement of the nodes is in such a way that we have two nodes at the top, followed by three nodes in the middle and two nodes at the bottom. The three nodes in the middle are the possible diseases the patient could be aﬄicted with; the two nodes at the top are conditions that could contribute to the likelihood of suﬀering from those diseases, while the two bottom nodes are the symptoms of those diseases. Conditional and marginal probability values are assigned to the nodes based on relevant information we have. These probability values are displayed in Table 3.1.

Table 3.1: Prior probabilities for chest illness diagnosis network.

A list of events for each node

1. A: Visit to Asia

2. S: Smoker

3. T: Has Tuberculosis

4. C: Has Lung Cancer

5. B: Has Bronchitis

6. TOC: Tuberculosis or Lung Cancer

23 7. XR: Positive X-ray

8. SB: Shortness of Breadth

After we construct the network, the software uses the clustering algorithm (or some other) to compute the marginal probabilities for each node; if we condition on some of the nodes, the software then calculates the posterior probabilities for each of the remaining nodes. Such marginal and posterior probabilities are displayed in Table 3.2. From the table, the marginal probability of the patient suﬀering from tuberculosis is about 1 percent, that of lung cancer is about 6 percent and bronchitis is about 45 percent. These marginals represent prior probabilities for the respective states. If we now suppose the X-ray result is abnormal and condition on that, the software calculates the posterior probability for tuberculosis to be about 9 percent, that of lung cancer to be about 49 percent and bronchitis to be about 51 percent. If, in addition to the abnormal X-ray result, we also condition on the presence of shortness of breadth, the software recalculates the posterior again and the probability of tuberculosis goes up to 11 percent, that of lung cancer goes up to 62 percent and that of bronchitis goes up to 68 percent. If we now know that the patient has been to Asia and add that to the condition, the posterior probability for tuberculosis jumps to 39 percent. Meanwhile the posterior for lung cancer is reduced from 62 percent to 44 percent and that of bronchitis falls from 68 percent to 63 percent. Finally, if we include the fact that the patient is a smoker, the posterior probability for tuberculosis falls to 29 percent, while that of lung cancer jumps to 58 percent and bronchitis jumps to 70 percent.

Table 3.2: Posterior probability values for Chest illness diagnosis.

Conditions Tuberculosis Lung Cancer Bronchitis None (marginal) 0.01 0.06 0.45 Abnormal X-ray 0.09 0.49 0.51 Abnormal X-ray + Shortness of Breadth 0.11 0.62 0.68 Abnormal X-ray + Shortness of Breadth + Visit to Asia 0.39 0.44 0.63 Abnormal X-ray + Shortness of Breadth + Visit to Asia + Smoker 0.29 0.58 0.70

24 3.2 Conditional Independence

We say that two events are independent of each other if the occurrence of one event does not affect the occurrence of the other. More precisely, for two events A and B, we say that A and B are independent if P(A|B)= P(A). We define conditional independence in a similar manner except that there is now a condition. Two events A and B are conditionally independent given a third event C if P(A|B,C)= P(A|C). In a similar fashion, we can define independence and conditional independence for random variables. Two random variables X and Y are said to be independent if P(X|Y ) = P(X); they are said to be conditionally independent given a third random variable Z if P(X|Y, Z)= P(X|Z). With these definitions, we can now present a more detailed discussion of Bayesian networks making use of the concept of conditional independence.

Let X = {X1,X2,...,Xn} be a collection of nodes each of which represents a discrete random variable Xi, with these nodes being connected according to a particular DAG

(directed acyclic graph). For each node Xi, let Yi be the set of nodes (possibly empty) which are the parents of Xi, and P(Xi|Yi) be the conditional probability of Xi given the values of its parents Yi. To say that the random variables are described by the DAG means that the joint distribution of X1,X2,...,Xn can be written as the product of conditional distributions: n

P(X)= P(Xi|Yi) (3.1) Yi=1 This product representation has important consequences for the relationships among the nodes. We shall say that two nodes are neighbors if there is a direct connection between them, i.e., one of the nodes is the parent (or child) of the other. We say that a path exists between two nodes Xi and Xj if there is a sequence of neighboring nodes which starts from

Xi and ends at Xj. (In traveling the path from Xi to Xj, the directions of the links (the arrows) are not important, only the fact that connections exist.) The product representation (3.1) implies the following general conditional independence property:

If U, V , and W are disjoint sets of nodes for which all paths from nodes in U to nodes in V pass through nodes in W , then U and V are conditionally independent given W .

25 We note that, if the ordering of the nodes X1,...,Xn is chosen so that parents always precede children, then the product in (3.1) is a special case of the chain rule

P(X)= P(Xi|Xi−1,Xi−2,...,X1) Yi=1 because in this case the conditional independence property stated above can be shown to imply that P(Xi|Xi−1,Xi−2,...,X1)= P(Xi|Yi).

3.2.1 Example 3

This is a simple example of a Bayes network obtained from a tutorial (see [1]) with four events, namely: Cloudy, representing whether it is cloudy or not; Rain, representing whether it is raining or not; Sprinkler, representing whether the sprinkler is on or not; and WetGrass, representing whether the grass is wet or not. The Bayesian network for this example is presented in Figure 3.3 below with its marginal and conditional probability tables.

26 Figure 3.3: A simple example (taken from [1])

A Simple Example

P(C=F) P(C=T) 0.5 0.5 Cloudy C P(R=F) P(R=T) F 0.8 0.2 T 0.2 0.8 Sprinkler Rain C P(S=F) P(S=T) F 0.5 0.5 T 0.9 0.1 WetGrass SR P(W=F) P(W=T) A complete model of a BN consists of: FF 1.0 0.0 • Structure (topology) of the graph. TF 0.1 0.9 • Conditional Probability Distributions FT 0.1 0.9 (CPD) at each node. TT 0.01 0.999

27 In this example, all nodes are binary; i.e. have two possible values denoted as T (for true) and F (for false). We can see that the event “grass is wet”’ (W=T) has two possible causes: either the water sprinkler is on (S=T) or it is raining (R=T). Since node C (Cloudy) has no parent, it is described by its marginal probabilities while the rest of the nodes are described by conditional probabilities, conditioning on their ancestors. By the chain rule of probability, the joint probability of all the nodes in the graph above can be written as:

P(C,S,R,W )= P(C)P(S|C)P(R|C, S)P(W |C,S,R)

Using conditional independence relationships, we can simplify this equation using the fact that R is independent of S given its parent C, and W is independent of C given its parents S and R. Therefore, we can re-write the above equation as follows:

P(C,S,R,W )= P(C)P(S|C)P(R|C)P(W |S, R)

For this example, we shall illustrate a probabilistic inference using the Bayesian network. Suppose we observe the fact that the grass is wet. There are two causes for this - either it is raining, or the sprinkler is on (or both). Which one is more likely depends on our posterior probabilities. We will use Bayes’ rule to compute the posterior probability of each explanation. First we note that:

P P (W = T )= c,s,r (C = c, S = s, R = r, W = T ) = 0.6471 P then,

P P C c,S T,R r,W T P (S=T,W =T ) c,r ( = = = = ) (S = T |W = T )= P(W =T ) = P P(W =T ) = 0.2781/0.6471 = 0.4298

P P C c,S s,R T,W P (R=T,W =T ) c,s ( = = = =1) (R = T |W = T )= P(W =T ) = P P(W =T ) = 0.4581/0.6471 = 0.7079

Based on the posterior probabilities, we can see that it is more likely that the grass is wet because it is raining than because the sprinkler is on; the likelihood ratio of which is

28 0.70790/0.4298 = 1.647. In this example, we notice that the two likely causes compete to explain the observed data, the grass is wet. Therefore S and R become conditionally dependent given that their common child, W, is observed, even though they are conditionally independent given their parent, C. For example, suppose that in addition to knowing that the grass is wet, we also know that it is raining. Then the posterior probability that the sprinkler is on goes down, i.e.

P P C c,S T,W T,R T P (S=T,W =T,R=T ) c ( = = = = ) (S = T |W = T, R = T )= P(W =T,R=T ) = P P(W =T,R=T ) = 0.1945

3.2.2 Variable Elimination

A graphical model such as a Bayesian network speciﬁes a complete joint probability distribution over all the variables. So, knowing the joint probability distribution, we can answer all possible inference questions by marginalization, i.e. summing out over irrelevant variables. If we assumed each node represents an event (can only have two states), the joint probability distribution has size 2n, where n is the number of nodes. This means that summing over the joint probability distribution will take an exponential amount of time. To do the marginalization eﬃciently, we use the factored representation of the joint probability distribution where we “push sums in” as far as possible when summing (marginalizing) out irrelevant terms. This process is called Variable Elimination. Here is an illustration of this process applied to the water sprinkler example discussed above:

P(W = w) = P(C = c, S = s, R = r, W = w) Xc Xs Xr = P(C = c)P(S = s|C = c)P(R = r|C = c)P(W = w|S = s, R = r) Xc Xs Xr = P(C = c) P(S = s|C = c) P(R = r|C = c)P(W = w|S = s, R = r) Xc Xs Xr With this process, as we perform the innermost sums, we create new terms, which need to be summed over in turn. For example,

P(W = w)= P(C = c) P(S = s|C = c) × T 1(c, w, s) Xc Xs

29 where

T 1(c, w, s)= P(R = r|C = c) × P(W = w|S = s, R = r) Xr If we continue in this way, we also have:

P(W = w)= P(C = c) × T 2(c, w) Xc where

T 2(c, w)= P(S = s|C = c) × T 1(c, w, s) Xs Having presented a brief introduction to Bayesian networks in this chapter, the next chapter will be devoted to the analysis of our case, the O.J. Simpson murder case making use of several of those networks in our analyses.

30 CHAPTER 4

Analysis

In the Introduction chapter, the framework for the analysis of this case was laid out; in this chapter, we shall carry out the analysis. However, before we begin the analysis, we will restate some pertinent parts of the framework necessary for the analysis. In the framework, we formulated the Ultimate probandum as:

This Ultimate Probandum needed to be proved - beyond reasonable doubt - by the prosecution to obtain the conviction of the accused, O.J. Simpson. From the Ultimate Probandum, we constructed ﬁve Penultimate Probanda (PP1 - PP5), each of which has to be proved, again - beyond reasonable doubt - in order to prove the Ultimate Probandum beyond reasonable doubt.

Although we have five probanda to be proved, the only one that was in dispute, as explained earlier, was PP5. Therefore, to prove the Ultimate Probandum, the prosecutor would need to prove - beyond reasonable doubt - that it was O.J. Simpson who inflicted the multiple stab wounds that killed both NBS and RLG. Hence from this point forward, our main task in this analysis is to evaluate the probative value of the entire mass of evidence in this case with the ultimate goal of proving the fifth Penultimate probandum, PP5. To do this, the entire body of evidence is partitioned into six different segments or categories, each of which contains several items of evidence.

31 A Bayesian network will be constructed for the collection of items of evidence in each segment and with the aid of the Hugin and GeNIe software, the aggregate probative force or strength of the evidence in each sector will be determined. Using Bayes rule, these sector- wise probative force assessments will be combined to determine the aggregate probative force for the entire body of evidence in this case. It should be noted here that the Bayesian networks constructed for the evidence sectors are subjective for two main reasons - the structure of the network and the assigned probabilities. For the structure, different people constructing a Bayesian network based on the same set of evidence items will construct different networks with different linkage patterns. The number of nodes in a network, the propositions that represent the random variables, and the qualitative arrangement of the nodes with the links would vary from person to person. For the probability assignments, it is also true that different individuals may have different feelings about the individual pieces of evidence, and may choose to assign different conditional probabilities, and thus would arrive at different Bayes nets. Once a linkage pattern is formulated for a particular network, the individual constructing the network will then assign conditional probabilities to every piece of evidence or testimony included in the analysis. These conditional probabilities will reflect the credibility and weight the user attaches to each piece of evidence or testimony; it is possible by varying the conditional probabilities to place greater or lesser importance on a particular piece of evidence or to disregard it completely. The reasoning and mental processes underlying the assignment of credibility to the individual pieces of testimony can be challenging, and sometimes subtle as long as, in the end, the user can come up with the required numbers (the conditional probabilities) which summarize their feelings about a particular piece of testimony. With testimonies, the conditional probability values assigned to a particular testimony may also reflect on the reliability placed on the witness by individual assigning the probabilities. In short, Bayesian networks might be regarded as a formal way for an individual to combine their separate judgments about the individual pieces of evidence in order to reach an overall judgment of the likelihood of guilt or innocence. This is what we set out to do in the next several sections of this chapter.

Before we begin the analysis, we would like to reiterate again that our approach is a form of statistical thought process that is very subjective - diﬀerent people might diﬀer in

32 formulation which will consequently produce varying results. Although there is a lot of mental processes involved in the formulation of a network and the assigned probabilities, the real life legal proceedings are characterized by more nuances and intangibles than what is present in our methodology. For example, the outcomes of a legal case does depend on factors such as the quality of Jury selection, and the lawyering skills from both sides of the case. Other factors may play a part too such as the investigative work, the police competence (incompetence), race, celebrity status or lack of, and money. In our present work, it is difficult to control for the effects of these qualitative factors that, more often, tend to influence the outcomes in legal cases. Furthermore, in the O.J. case, he was charged with only one crime - first degree murder in the death of Nicole Simpson and Ron Goldman; in our analysis, we analyzed the evidence against the first degree murder charge as contained in our ultimate probandum. However, in many criminal cases, the accused are charged with more than one crime and Juries are also instructed by the court to consider “Lesser Included Offenses” (LIO) if they are not able to come to an agreement on the main offense. A lesser included offense is an offense which all of its elements are contained in the main offense but which does not contain all of the elements of the main offense. In other words, all of the elements of a LIO are a subset of the elements of the main offense. For example, a crime of manslaughter or a second degree murder will be a LIO of the crime of first degree murder.

4.1 Motives

As explained above, the challenge for the prosecution was to prove that it was O.J. Simpson who committed the two murders. A logical place to start would be for the prosecution to develop a credible theory to explain to the jury why O.J. would have committed such a heinous crime. In other words, the prosecution needed a credible motive for O.J.’s actions. Although the prosecution does not need to prove motive in a criminal case as it is usually not part of the required elements of the law, in many cases it is extremely diﬃcult, if not impossible, to persuade a jury to convict the accused without providing a persuasive reason why he committed the crime. In the O.J. Simpson case, the prosecution, among competing theories for motives, elected to go with the “theory of control” as summarized below: (see [7], pg.119)

33 OJS had expressed jealous rage resulting in violence in his attempts to control NBS and prevent her from ﬁnally severing their relationship. His continuing jealous rage gave him a motive to murder her as the ultimate act of control, and the brutal manner in which she was murdered by multiple stab wounds shows that she was murdered by someone acting in a rage. He had a motive to try to maintain his control and to prevent NBS from acting independently, and he went to her house to kill her as the ultimate act of control. Therefore, it was OJS who murdered NBS in a jealous rage.

The theme of this evidence segment is the theory of control as the motive for the murder by O.J. Simpson: O.J. was controlling and wanted to control Nicole and killing her was the ∗ ultimate control for O.J. Simpson. In this evidence segment denoted by E1 , all the evidence items relating to the motives of the accused to commit the murder are collected together and used, with the aid of several interim probanda, to construct a Bayesian network using the Hugin software. The list of the evidence items and the interim probanda is presented on page 36, the probability table is presented in Table 4.1, and the resulting network is presented in Figure 4.1. The network consists of fourteen nodes connected by links. At the top of the network is the node representing the penultimate probandum PP5 (OJ committed the two ∗ ∗ ∗ ∗ ∗ ∗ murders) denoted as H5 while the evidence nodes (B , C , D , F , G1, G2) are at the bottom ∗ ∗ of the network. The evidence subset E1 is the conjunction of these evidence nodes; that is, E1 ∗ ∗ ∗ ∗ ∗ ∗ = B ∩C ∩D ∩F ∩G1 ∩G2. These evidence nodes are connected to H5 by arrays of interim probanda (or hypotheses) representing several stages of reasoning. Each link in the chain of reasoning exposes a source of doubt concerning the probative strength of the evidence on H5.

In Table 4.1, we started our probability assignments with the node at the top of the network (a root node) by showing our indiﬀerence to the proposition that OJ committed the two murders, to which we assign a probability of 0.5 and a probability of 0.5 to its complement (It was not OJ who committed the two murders). To prove H5, we connect two nodes right below it: the ﬁrst one is the node representing A which represents the fact that OJ probably killed NBS because he wanted to control her and killing her was the ultimate act of control; the second one is the node representing B which represents the proposition “OJ

34 beat NBS”. Here, we believe that if OJ committed the murders, it was highly probable that he was also physically abusive towards his ex-wife, especially because their relationship was a rocky one with a documented history of allegations of abuse; therefore, we set P(B|H5) = 0.85. We also recognize that there are a lot of men who are physically abusive towards their wives but never killed them; for this reason, we suppose that even if O.J. did not commit the murders, he could still have been abusive towards his ex-wife but with a small probability. P c In this case, we set (B|H5) = 0.01. We inferred from Nicole’s 911 call of October 25th 1993 that there was some type of physical abuse going on in her relationship with O.J., especially when she told the dispatcher that “He’s going to beat the (expletive) out of me”; so we set P(B∗|B) = 0.65 and P(B∗|Bc) = 0.05. By deﬁnition, if you beat your wife, that’s an abuse; so, we concur here that if O.J. beat his wife, he was abusive with certainty; therefore, we set P(D|B) = 1.00. But we set P(D|Bc) = 0.01 reﬂecting the fact that even if O.J. did not beat his wife, he might have been abusive in other ways (i.e. emotional). We believe that the content of Nicole’s 911 call was a strong evidence of O.J.’s abuse towards his wife and consider it very unlikely that Nicole would make such a call without any abuse going on; so, we set P(D∗|D) = 0.98 and P(D∗|Dc) = 0.01. The rest of our probability assignments are displayed in Table 4.1. In total, there are thirty-four such probability values assigned to fourteen stages of reasoning in this network. These probabilities and the structure of the network determine the prior probabilities of all the events (represented by nodes in the network). These probability values in Table 4.1 are fed into the Hugin software and after conditioning on the evidence nodes, we then run the Bayesian network algorithm after which we refer to the network as being compiled. The software will now update the probability values at each of the nodes in light of the evidence. These updated probability values are ∗ now the posterior probabilities for each node; that is, the probabilities conditional on E1 . A table of posterior probabilities for each node is displayed in Table 4.2.

∗ From chapter 2 above and eqns (2.7), (2.8) and (2.13), we can write LE1 as: P ∗ P c (H5|E1 ) (H5) LE∗ = (4.1) 1 P c ∗ P (H5|E1 ) (H5) We can now use equation (4.1) to calculate the likelihood ratio of the evidence under c the propositions H5 and H5. Recall H5 is the proposition that it was O.J. Simpson who c committed the two murders, whereas H5 is the proposition that it was not O.J. Simpson

35 who committed the two murders. In equation (4.1), the likelihood ratio is a product of two ratios: the numerator of the ﬁrst ratio is the posterior probability of H5 under the entire collection of evidence regarding motives while the denominator is the posterior probability c of H5 under the same evidence. The second ratio on the right hand side of equation (4.1) c consists of priors for our two propositions H5 and H5. For these, we had decided in the beginning to use non-informative priors by setting each one to be 0.5; in this case, those two priors drop out and the likelihood ratio calculation reduces to the ratio of the two posterior probabilities. These two posterior probabilities can be obtained from the compiled network. P ∗ P c ∗ For our network of evidence related to motives, (H5|E1 ) = 0.9885, (H5|E1 ) = 0.0115, and

∗ their ratio, LE1 = 85.96. This means it is about 86 times as likely to obtain the evidence in this collection if we suppose O.J. Simpson committed the two murders than if we suppose he did not commit the two murders.

A List of propositions and evidence items for Motives:

1. H5: O.J. committed the two murders

2. A: O.J. wanted to control NBS

3. B: O.J. beat NBS

4. B∗: Nicole’s 911 call tape of October 25, 1993 (testimony to B)

5. C: O.J. did not want Nicole to date other men

6. C∗: NBS ex-boyfriend, Keith’s testimony to C

7. D: O.J. was abusive

8. D∗: Nicole’s 911 call tape of October 25, 1993 (testimony to D)

9. E: O.J. displayed jealous rage towards NBS

10. F: O.J. was stalking NBS

11. F ∗: NBS ex-boyfriend, Keith’s testimony to F

12. G: O.J. was intimidating NBS and friends

36 ∗ 13. G1: NBS ex-boyfriend, Keith’s testimony to G

∗ 14. G2: Nicole’s 911 call tape of October 25, 1993 (testimony to G)

Table 4.1: Prior probabilities for propositions relating to O.J. Simpson’s Motives for the murder.

Prob. Values Prob. Values P P c c (H5) 0.5 (E|C H5) 0.01 P c P ∗ (H5) 0.5 (D |D) 0.98 ∗ c P(A|BH5) 0.95 P(D |D ) 0.01 P c P (A|BH5) 0.80 (E|CH5) 0.90 P c P c (A|B H5) 0.70 (E|CH5) 0.40 P c c P (A|B H5) 0.02 (F |E) 0.90 c P(B|H5) 0.85 P(F |E ) 0.001 P c P (B|H5) 0.01 (G|FE) 0.999 P(B∗|B) 0.65 P(G|FEc) 0.80 P(B∗|Bc) 0.05 P(G|F cE) 0.9 P(C|A) 0.80 P(G|F cEc) 0.1 P(C|Ac) 0.15 P(F ∗|F ) 0.97 P(C∗|C) 0.98 P(F ∗|F c) 0.01 P ∗ c P ∗ (C |C ) 0.001 (G1|G) 0.97 P P ∗ c (D|B) 1.00 (G1|G ) 0.01 P c P ∗ (D|B ) 0.10 (G2|G) 0.99 P c P ∗ c (E|C H5) 0.85 (G2|G ) 0.05

37 Table 4.2: Posterior probabilities for propositions relating to O.J. Simpson’s Motives for the murder.

Nodes Nodes Prob. Values O.J. Committed the two murders H5 0.9885 O.J. wanted to control NBS A 0.9881 O.J. beat NBS B 0.9969 O.J. did not want Nicole to date other men C 0.9999 O.J. was abusive D 0.9997 O.J. displayed a jealous rage E 0.9998 O.J. was stalking Nicole F 0.9988 O.J. was intimidating Nicole and her friends G 1.0000

Figure 4.1: A Bayesian Network for Motives

OJ committed the two murders (H5)

OJ wanted to control NBS (A) OJ beat Nicole (B)

OJ did not want OJ displayed a Nicole to date jealous rage (E) other men © Nicole’s 911 OJ was call of Oct. abusive (D) 25th 1993 (B*)

OJ was OJ was intimidating NBS ex-boyfriend, stalking NBS and Keith’s testimony NBS (F) (C*) friends (G) Nicole’s 911 call of Oct. 25th 1993 (D*)

Keith’s Nicole’s 911 call Keith’s testimony of Oct. 25th 1993 testimony ( F*) (G2*) (G1*)

38 4.2 Opportunity to commit the murders

In this section, we turn to the analysis of a collection of evidence we feel pertain to the existence of opportunities for O.J. Simpson to have committed the murders. For this subset of evidence, a Bayesian network was constructed comprising of 49 nodes representing diﬀerent stages of reasoning. Unlike the collection of evidence for other categories, this network is fairly large, with the list of evidence items and all the interim probanda presented below. As with the network for Motives, we locate at the top of this network the node representing our penultimate probandum H5, i.e. O.J. committed the two murders. This node was connected to several evidence items through a constellation of interim probanda representing diﬀerent stages of reasoning. Here, we shall denote the collection of all evidence items in this category ∗ as E2 which represents the intersection of all the evidence nodes (those with asterisked labels). For the analysis, probability values were assigned to each node representing prior c probabilities; again, we assigned probability of 0.5 each to H5 and H5 at the top node. In all, 118 prior probability values were assigned to the 49 nodes. Given the size of this network, it would be a daunting task to try to indicate and comment on the probability values assigned to each node; however, a table of those probability values (priors) is presented in Table 4.3 with the corresponding network for this subset of evidence shown in Figure 4.2. The list of the evidence items and the interim probanda is presented on page 42. For the analysis, our main focus here is the posteriors for the top node, our penultimate probanda. After running P ∗ P c ∗ the default algorithm in the GeNIe software, we obtained (H5|E2 ) = .9850 and (H5|E2 )

∗ = .0150. As we did with all the previous evidence categories, we calculated LE2 = 65.67, c the likelihood ratio under H5 and H5. This means it is about 66 times as likely to obtain the evidence in this collection if we suppose O.J. Simpson committed the two murders than if we suppose he did not commit the two murders.

Although comments on each assigned probability values and the details of how this evidence network was constructed were not provided due to the size of the network, we shall provide a general overview of the evidence items here and their signiﬁcance in the grand scheme of our analysis. The evidence items charted in this sector are to establish the fact that O.J. Simpson had the opportunity to have committed the murders based on the testimonies of major witnesses here and some known time lines. Although there were

39 testimonies from other witnesses used in this sector, the more significant testimonies came from three individuals: Mr. Brian (Kato) Kaelin, the guest living in one of the guest units at O.J.’s Rockingham residence, Mr. Allan Park who was the limo driver who drove O.J. to the Airport to catch an 11:45 p.m. flight to Chicago, the night of the murder, and finally Ms. Shively, a resident of Brentwood California (O.J. and Nicole’s neighborhood) who claimed to have seen O.J. driving his white Ford Bronco around the estimated time of the murder.

First, through phone records, the prosecution was able to establish that Nicole spoke to her mother the night of the murder at 9:40p.m. which would establish that Nicole was killed sometimes after 9:40p.m. on that night. In its opening statement, the prosecution suggested that the murders were committed between 9:45 p.m. and 10:50 p.m. the night of the murder. Mr. Pablo Fenjves who testiﬁed on behalf of the prosecution claimed that he heard a dog started barking and wailing around Nicole’s house between 10:15 p.m. and 10:20 p.m. the night of the murder, and incessantly for a very long time. This testimony led the prosecution to narrow the estimated time of death to about 10:15 p.m. that night. Another resident of Brentwood California, Mr. Steven Schwab, testiﬁed that while he and his wife were walking their dog at night, they discovered a large Akita dog wandering around at about 10:55 p.m. which they observed to have blood on all its four paws and turned out to be Nicole’s dog. According to Mr. Schwab’s testimony, the dog followed them home, and not knowing what to do with the dog, they handed over the dog to another neighbor, Mr. Sukur Botzepe. It was the dog that led Mr. Sukur and his wife to the bodies of the two victims, Nicole and Ron Goldman, lying in the courtyard of Nicole.

So far, we know that Nicole was alive at 9:40 p.m. the night of the murder and the prosecution estimated that the murders were committed that night between 9:45 p.m and 10:50 p.m. We also know that Nicole’s dog was discovered at about 10:55 p.m with blood on its paws from which we can infer that by 10:55 p.m. that night, the murders have already been committed. Now, during this window of about an hour and ﬁfteen minutes (9:40 - 10:55p.m), the whereabouts of O.J. Simpson were not known, and with no established alibi: Kato Kaelin testiﬁed that on the night of the murder, he and O.J. went to a nearby McDonald to get some food and when they came back home, he parted with O.J. between 9:30 and 9:35 p.m. and never saw O.J. again until around 11:00p.m that night when O.J. was getting

40 ready to go to the Airport. Nobody else seemed to see O.J. or know his whereabouts during that time period except Ms. Shively who claimed to have seen O.J. on the road in that time interval. Ms. Shively testiﬁed that between 10:48 p.m. and 10:50p.m, the night of the murder, O.J. driving his white Ford Bronco almost collided with her and another car when O.J. was trying to run a red light at the intersection of San Vicente blvd. and Bundy drive in Brentwood. That intersection was a point along the route from Nicole’s house (the crime scene) and O.J.’s Rockingham residence. She said that on that night, she and the other car were driving in opposite direction on San Vicente blvd; with the green light on their side, they attempted to cross the intersection of Bundy when a white Ford Bronco driving on Bundy attempted to run through the intersection but was stopped by the presence of her car and the other car at the intersection. She said that this incident almost resulted in a three-car collision at the intersection, and that when the Bronco came to almost a complete stop, the driver of the Bronco was angry, yelling and cursing at the driver of the other car. At that point, she was able to identify the driver of the white Bronco to be O.J. Simpson whom she had seen many times in the neighborhood and also on TV.

The limo driver, Mr. Allan Park, who drove O.J. to the Airport the night of the murder also testiﬁed on behalf of the prosecution. He testiﬁed that he was instructed to pick up O.J. at his Rockingham residence and drove him to the Airport. The driver got to O.J.’s residence a little early, around 10:25 p.m. At about 10:40 p.m., he got out of the car and rang the bell to the house repeatedly without any response. At 10:50 p.m., he called his boss to inform him that he didn’t think that anyone was in the house because of lack of response to his repeated pressing of the bell. At about 10:55 p.m., the driver saw a black man at a distance inside the residence walking briskly towards and eventually entered the main house; the driver then proceeded to ring the bell again at which time O.J. answered and told the driver that he overslept. This contradicts the testimony of Ms. Shively above who claimed to have seen O.J. on the road about ten minutes earlier and almost got into an accident because of his reckless driving. Shortly after 11:00 p.m. that night, the limo driver took O.J. to the Airport.

From above, the guest living at O.J. house, Mr. Kaelin testiﬁed that he parted with O.J. the night of the murder between 9:30 and 9:35 p.m. after they came back from McDonald to get some food. According to Mr. Kaelin, when he left O.J., he went back to his room and

41 after he finished with his food, he made a call to a friend. Later, he called his girlfriend and while he was on the phone with his girlfriend, he heard about three loud bangs in the back of his room. The force of the bangs were strong enough to shake the picture hanging on the wall of his room. At that time, he thought that maybe they just had an earthquake or an intruder just entered the property through the back alley behind his room. To confirm his suspicion, he asked his girlfriend immediately if they just had an earthquake, to which she said no. He then thought that if what he heard and felt was not from an earthquake, perhaps an intruder just the premise. He then told his girlfriend that he was going outside to check the source of the bang and if she did not hear back from him in ten minutes, she should call the police. With a small flashlight, Mr. Kaelin then went into the yard to check the back of his room but before he went too far, he saw the limo by the gate waiting to take O.J. to the Airport. He approached the limo driver and asked him if he felt an earthquake and the driver also said no. He opened the gate for the driver to pull in the limo and later saw O.J. came out of the main house. He then asked O.J. the same question regarding earthquake and O.J. reaffirmed what the other two people had said - there was no earthquake. Mr. Kaelin was so disturbed by whatever shook the picture from the back of his room that he asked O.J. to go with him to the check the small walk-way behind his room just in case there was an intruder on the property. Needless to say, O.J. declined to assist because he needed to hurry and get to the Airport.

All of the testimonies described here were marshalled together to construct the network for this sector. The established timeline of the murder; the behavior of the dog that suggested that something bad has happened and the ultimate discovery of the bodies. Furthermore, the apparent disappearance of O.J. during the period in which the murder was committed; the apparent lack of response to the limo driver’s repeated pressing of the bell at O.J’s house which led the limo driver to believe that there was nobody home; the bangs that shook the picture on the wall of Kato’s room which led him to believe that there was either an earthquake or an intruder on the property and the subsequent re-emergence of O.J. at the end suggest that O.J. had enough opportunity to have committed the murder. We should also point out that the driving distance from Nicole’s house (the crime scene) and O.J.’s Rockingham residence is just about six minutes.

42 List of propositions and evidence items for Opportunity to commit the murders

1. H5: O.J. committed the two murders

2. A: The murders were committed between 9:45p.m. and 10:50 p.m. at NBS’ house

3. B: O.J. was at Nicole’s house sometime between 9:45 p.m. and 10:50 p.m. the night of the murder

4. C: Nicole spoke to her mom on the phone at about 9:40 p.m. the night of the murder

5. C∗: Prosecution/phone records

6. D: NBS and RLG were killed at about 10:15p.m. at NBS’ house the night of the murder

7. E: A dog was barking and wailing around Nicole’s house between 10:15 p.m. and 10:20p.m.

8. E∗: Pablo Fenjves testimony to E

9. F: Nicole’s large Akita dog was found wandering around with bloody paws at about 10:55 p.m.

10. F ∗: Steven Schwab’s testimony to F

11. G: Akita dog led Sukru back to NBS’ house

12. G∗: Sukru’s testimony to G

13. H: O.J. ﬂed from the murder scene as quickly as possible in a white Ford Bronco

14. I: O.J. owns a white Ford Bronco

15. J: O.J. was seen at the intersection of San Vicente Blvd. and Bundy Drive (a point between the crime scene and O.J.’s residence) between 10:48 p.m. and 10:50 p.m. driving a white Ford Bronco

16. J ∗: Ms. Shively’s testimony to J

17. K: O.J. ran a red light at the intersection of San Vicente Blvd. and Bundy Dr.

43 18. K∗: Ms. Shively’s testimony to K

19. L: O.J. almost caused a three-car collision at the intersection of San Vicente Blvd. and Bundy Dr.

20. L∗: Ms. Shively’s testimony to L

21. M: O.J. left the intersection of San Vicente and Bundy to go home

22. N: O.J. was taking a ﬂight to Chicago at 11:45p.m.

23. N ∗: Limo driver’s testimony to N

24. O: Limo driver was instructed to pick up O.J. from his residence at 10:45 p.m.

25. O∗: Limo driver’s testimony to O

26. P: O.J. was not home between 9:45 p.m. and 10:50 p.m. but returned shortly after

27. P ∗: Kato’s testimony to P

28. Q: To avoid being seen by the Limo driver, OJ snuck back onto his property through a neighbor’s property after 10:25 p.m.

29. R: O.J. passed by the back of the guest houses on his way to the main house sometime after 10:25 p.m.

30. S: O.J. made a violent contact with the air-conditioning unit in the wall of Kato’s guest room

31. T: Kato believed there was an earthquake

32. T ∗: Kato’s testimony to T

33. U: The violent contact with the air-conditioner shook the picture on the wall of Kato’s guest room

34. U ∗: Kato’s testimony to U

35. V: Kato asked the Limo driver if he felt an earthquake

44 36. V ∗: Limo driver’s testimony to V

37. W: Kato asked his girlfriend if they just had an earthquake during their phone conversation

38. W ∗: Kato’s testimony to W

39. X: Kato told O.J. about the noise he heard from the back of his room and asked O.J. If they just had an earthquake

40. X∗: Kato’s testimony to X

41. Y: There was nobody home when Limo driver arrived at 10:25 p.m.

42. Z: No response when limo driver rang the door bell at O.J.’s residence the ﬁrst time at 10:40p.m. which led him to call his boss at 10:50 p.m. and tell him he didn’t think O.J. was home

43. Z∗: Limo driver’s testimony to Z

44. A1: No light downstairs and only one light upstairs

∗ 45. A1: Limo driver’s testimony to A1

46. A2: O.J. left for Nicole’s house after he parted with Kato

47. A3: O.J. had the opportunity to commit the murders

48. A4: Kato parted with O.J. between 9:40 p.m. and 9:45p.m. and did not see him again until 11:00 p.m. the night of the murder

∗ 49. A4: Kato’s testimony to A4

45 Table 4.3: Prior probabilities for propositions relating to O.J. Simpson’s Opportunity to commit the murders.

No. Prob. Values Prob. Values Prob. Values Prob. Values ∗ 1 P(H5) 0.5 P(H|B) 0.95 P(O |O) 0.99 P(X|T ) 0.85 c c ∗ c c 2 P(H5) 0.5 P(H|B ) 0.15 P(O |O ) 0.001 P(X|T ) 0.02 ∗ 3 P(A|H5) 0.90 P(I|HJ) 0.90 P(P |B) 1.00 P(X |X) 0.98 c c c ∗ c 4 P(A|H5) 0.40 P(I|HJ ) 0.85 P(P |B ) 0.25 P(X |X ) 0.20 c ∗ 5 P(B|H5A) 1.00 P(I|H J) 0.85 P(P |P ) 0.95 P(Y |P ) 0.70 c c c ∗ c c 6 P(B|H5A ) 0.20 P(I|H J ) 0.10 P(P |P ) 0.10 P(Y |P ) 0.00 c 7 P(B|H5A) 0.02 P(J|HP ) 0.80 P(Q|P ) 0.95 P(Z|Y ) 1.00 c c c c c 8 P(B|H5A ) 0.20 P(J|HP ) 0.00 P(Q|P ) 0.00 P(Z|Y ) 0.02 9 P(C|A) 0.60 P(J|HcP ) 0.05 P(R|Q) 0.70 P(Z∗|Z) 0.999 10 P(C|Ac) 0.10 P(J|HcP c) 0.00 P(R|Qc) 0.30 P(Z∗|Zc) 0.0001 ∗ 11 P(C |C) 0.98 P(K|JI) 0.15 P(S|R) 0.80 P(A1|YP ) 0.85 ∗ c c c c 12 P(C |C ) 0.02 P(K|JI ) 0.15 P(S|R ) 0.00 P(A1|YP ) 0.00 c c 13 P(D|A) 0.98 P(K|J I) 0.00 P(T |SU) 0.98 P(A1|Y P ) 0.10 c c c c c c 14 P(D|A ) 0.00 P(K|J I ) 0.00 P(T |SU ) 0.90 P(A1|Y P ) 0.95 ∗ c ∗ 15 P(E|AD) 0.95 P(K |K) 0.95 P(T |S U) 0.05 P(A1|A1) 0.90 c ∗ c c c ∗ c 16 P(E|AD ) 0.75 P(K |K ) 0.02 P(T |S U ) 0.05 P(A1|A1) 0.10 c ∗ 17 P(E|A D) 0.00 P(L|JK) 0.80 P(T |T ) 0.98 P(A2|BP ) 1.00 c c c ∗ c c 18 P(E|A D ) 0.05 P(L|JK ) 0.20 P(T |T ) 0.10 P(A2|BP ) 1.00 ∗ c c 19 P(E |E) 0.98 P(L|J K) 0.00 P(U|S) 0.80 P(A2|B P ) 0.00 ∗ c c c c c c 20 P(E |E ) 0.05 P(L|J K ) 0.00 P(U|S ) 0.00 P(A2|B P ) 0.00 ∗ ∗ 21 P(F |EA) 0.95 P(L |L) 0.95 P(U |U) 0.99 P(A3|B) 0.70 c ∗ c ∗ c c 22 P(F |EA ) 0.80 P(L |L ) 0.01 P(U |U ) 0.01 P(A3|B ) 0.00 c 23 P(F |E A) 0.60 P(M|J) 0.90 P(V |T ) 0.98 P(A4|A2A3) 0.60 c c c c c 24 P(F |E A ) 0.02 P(M|J ) 0.70 P(V |T ) 0.05 P(A4|A2A3) 0.60 ∗ ∗ c 25 P(F |F ) 0.98 P(N|M) 0.60 P(V |V ) 0.95 P(A4|A2A3) 0.00 ∗ c c ∗ c c c 26 P(F |F ) 0.001 P(N|M ) 0.40 P(V |V ) 0.04 P(A4|A2A3) 0.10 ∗ ∗ 27 P(G|F ) 0.98 P(N |N) 0.95 P(W |T ) 0.95 P(A4|A4) 0.90 c ∗ c c ∗ c 28 P(G|F ) 0.00 P(N |N ) 0.02 P(W |T ) 0.20 P(A4|A4) 0.05 29 P(G∗|G) 0.99 P(O|N) 0.95 P(W ∗|W ) 0.95 P(J ∗|J) 0.85 30 P(G∗|Gc) 0.05 P(O|N c) 0.002 P(W ∗|W c) 0.20 P(J ∗|J c) 0.15

46 Table 4.4: Posterior probabilities for propositions relating to O.J. Simpson’s Opportunity to commit the murders.

Nodes Nodes Values O.J. Committed the two murders H5 0.9850 The murders were committed between 9:45p.m. and 10:50p.m ... A 0.9990 OJ was at Nicole’s house between 9:45p.m. and 10:50p.m. ... B 0.9940 Nicole spoke to her mom on the phone at 9:40 p.m. the night ... C 0.9860 NBS and RLG were killed about 10:15 p.m at NBS’ house the ... D 0.9830 A dog started barking and wailing around Nicole’s house ... E 0.9980 Nicole’s large Akita dog was found wandering around with ... F 1.0000 Akita dog led Sukur back to NBS’ house G 0.9990 O.J. ﬂed from the murder scene as quickly as possible in a ... H 0.9950 O.J. owns a white Ford Bronco I 0.9000 O.J. was seen at the intersection of San Vicente Blvd. and ... J 1.0000 O.J. ran a red light at the intersection of San Vicente Blvd and ... K 0.9700 O.J. almost caused a three-car collision at the intersection of ... L 0.9960 O.J. left the intersection of San Vicente and Bundy to go home M 0.9310 O.J. was taking a ﬂight to Chicago at 11:45p.m. N 1.0000 Limo driver was instructed to pick up O.J. from his residence O 1.0000 O.J. was not at home at the time of the murder P 1.0000 To avoid being seen by the Limo driver, O.J. snuck back onto ... Q 0.9780 O.J. passed by the back of the guest houses on his way to the R 1.0000 O.J. made a violent contact with the air-conditioning unit in the ... S 0.9990 Kato believed there was an earthquake T 1.0000 The violent contact with the air-conditioner shook the picture on ... U 0.9970 Kato asked the Limo driver if he felt an earthquake V 0.9990 Kato asked his girlfriend if they just had an earthquake during ... W 0.9890 Kato asked O.J. if they just had an earthquake X 0.9650 There was nobody home Y 0.9980 No response when limo driver rang the door bell at O.J.’s residence ... Z 1.0000 No light downstairs and only one light upstairs A1 0.9800 O.J. left for Nicole’s house after he parted with Kato A2 0.9940 OJ had the opportunity to commit the murders A3 0.6960 Kato parted with OJ between 9:40 and 9:45 p.m. ... A4 0.9570

47 Figure 4.2: A Bayesian network for Opportunity to commit the murders

A B C A2

H A4 A1 D C* P

A4* Y A1*

E F J Q Z I J* Z* P* E* F* M R G S L K

N G* T U L* K* T*

O N* V U* W X

O* V*

W* X*

48 4.3 The Gloves

As explained in the section on the category of evidence items collectively referred to as knowledge of guilt evidence, criminals very often would leave behind, among others, some physical evidence at the crime scene, and the crime scene in O.J. Simpson’s case was no exception. At the crime scene, where Nicole and her friend, Ron Goldman, were brutally murdered, the police officers who first responded to the scene found a left-handed bloody glove believed to have been inadvertently left behind by the assailant. Within a few hours of the discovery of the left-handed glove at the crime scene, another glove, a right-handed one, was found by the L.A. detectives at O.J. Simpson’s residence that was believed to be the matching hand of the left glove. The prosecution argued that it was O.J. Simpson who committed the crime, and mistakenly dropped the left hand glove at the crime scene since the right hand glove was found on the premise of his residence. The defense on the other hand rejected the prosecution’s theory, and denied O.J.’s involvement in the murder. The defense insinuated that the investigating officers discovered both gloves at the crime scene and decided to plant the right hand glove at the O.J.’s residence in order to frame him. The probabilistic story we set out to tell in this section relates to these two famous (infamous) gloves and other ancillary evidence items connected to them. All evidence items in this sector ∗ are collectively referred to as “The gloves” and denoted by E3 . With the aid of propositions to connect the gloves evidence items to our main hypothesis, we shall construct a network for this evidence category and evaluate the probative force of the collection of such evidence items. The list of the evidence items and the interim probanda is presented on page 56, the prior probability table is presented in Table 4.5, and the resulting network is presented in Figure 4.3.

The network constructed for this category of evidence consists of twenty three nodes with connecting links. As usual, we started the net with a root node at the top representing c our main hypothesis H5 (O.J. committed the two murders) and its complement, H5 (It was someone other than O.J. who committed the two murders). These two hypotheses were assigned a non-informative prior of 0.5 each. One of the ﬁngers that points to O.J. as being the assailant in this murder case was a left hand glove found at the crime scene believed to belong to O.J.; so, to prove our main hypothesis, we have a proposition relating to this glove

49 right below it. Given that O.J. committed the two murders (event H5), we suppose there is a high probability that the left hand glove discovered at the murder scene belongs to him

(event A). Hence we have P(A|H5) = 0.90. By the same token, we suppose that if O.J. did not commit the two murders, it would be highly unlikely that the left hand glove found at P c the murder scene belongs to him; therefore we set (A|H5) = 0.01.

The Los Angeles police officer who first arrived at the crime scene and is credited with the discovery of the left hand glove at the crime scene was Officer Riske. He testified to this discovery and also to the fact that after securing the crime scene, he later told the L.A. detectives who arrived a few hours later about the glove and showed them its specific location at the crime scene. The L.A. detectives also testified to this discovery. We put a lot of credence in the testimony of Officer Riske and that of L.A. detectives regarding the discovery and specific location of this glove. To disbelieve Officer Riske is to suggest that he planted the left hand glove at the crime scene himself; given the totality of the circumstances, we do not believe in such a scenario. Since the glove was discovered a few hours before the arrival of the detectives and was shown to them on their arrival, we do not believe the detectives had anything to do with the planting of the glove either and therefore P ∗ P ∗ believe their testimonies. Based on our explanation, we have (A1|A) = 0.98 and (A2|A) = 0.95. For all the witnesses here, we do not believe that they would provide that testimony P ∗ c P ∗ c about the event if it didn’t occur. Therefore, we have (A1|A ) = 0.01 and (A2|A ) = 0.10.

In this criminal case, nothing garnered more attention than a right hand glove that was allegedly found on the Rockingham premise of O.J. Simpson by the L.A. detectives a few hours after the discovery of the left hand glove at the crime scene. According to testimony, one of the detectives, Mark Fuhrman, first found the glove at a remote part of the premise while conducting a walk-through of the premise and immediately called the attention of the other three detectives who were on the premise with him. However, this piece of evidence generated such a huge controversy because the detective, Mark Fuhrman, was a white law enforcement officer who had made disparaging remarks about blacks and black offenders in the past but denied making such remarks on the witness stand while under oath until an audio tape evidence surfaced that proved otherwise. And because the accused, O.J. Simpson, was a black man, many people particularly in the black community believed that

50 Mark Fuhrman planted the right hand glove on O.J.’s premise in order to frame him for the murders. Taking an objective stand, we feel that if a left hand glove was found at the crime scene with any evidence (such as matching blood type) to suggest it might belong to O.J., it is highly possible that a right hand glove could be found at O.J. Simpson’s residence (node B) without being planted by a third party. So, we assigned 0.80 to P(B|A) and a low value of 0.02 to the P(B|Ac) because we believe it will be rare to find the right hand glove in O.J.’s residence if he had no contact with the murder scene. As apparent in our network, node C has two “parents” or sources of probabilistic influence, nodes A and B. That means that whether the two gloves are a matching pair depends upon whether the left hand glove found at the crime scene belongs to O.J. and upon whether the right hand glove was discovered at O.J.’s residence. This type of probabilistic influence construct requires that we specify the following prior conditional probabilities: P(C|AB), P(C|AcB), P(C|ABc), P(C|AcBc). We suppose that it is highly probable that the two gloves are a matching pair given that the glove found at the crime scene was a left hand, brown leather that belongs to O.J. Simpson and the right hand was brown leather and was found at O.J.’s residence. So, we set P(C|AB) = 0.95. However, if no brown leather glove was found at the crime scene and no brown leather glove was also located at O.J.’s residence, then the intersection of events Ac and Bc would exclude the possibility of C which requires that we set P(C|AcBc) = 0. Even if a brown leather glove was located at the crime scene but no other glove was found at O.J.’s residence or anywhere else, there would be no comparison to be made; by the same token, if the right hand glove was found at O.J.’s residence but no left hand glove found at the crime scene, there would be nothing to compare. Therefore P(C|AcB) = P(C|ABc) = 0.

After the right hand glove was found at O.J. Simpson’s residence, the detectives believed that it was the right hand mate of the left hand glove that was discovered at the crime scene. This belief may be due to the fact that the two gloves were both made of brown leather, appeared to be the same size, and they were of opposite hands. However, we recognize that none of the detectives were experts in leather gloves but their beliefs might have come from sound years of detective experience and perhaps that of intelligent laypersons. That notwithstanding, we assigned probability of 0.65 to the testimony of the detectives that the ∗ two gloves were indeed a matching pair (node C1 ) given the event that the two gloves were

51 actually a match (node C). What about if the two gloves were not even a match? In their zealous detective work, the detectives might erroneously believe that the two gloves were P ∗ c actually a match; for this, we set (C1 |C ) = 0.30. There were other witnesses’ testimonies regarding the matching gloves that we believe deserve more credibility. First, Ms. Brenda Vemich, an employee of Bloomingdales departmental store in New York city who was a sales associate in the glove department, who also sold two pairs of gloves similar to those in evidence to Nicole, O.J.’s ex-wife, testified that the two gloves were a matching pair. P ∗ We assigned her hit probability, (C2 |C), a high value of 0.90 because we suppose she will have a lot of familiarity with gloves given that she was selling them on a regular basis as a sales associate in the glove department. Her judgment regarding whether two gloves are a matching pair will be closer to the truth compared to a layperson on the street. Another witness we found credible was Mr. Richard Rubin, the former Vice President and General Manager of Aris Isotoner, the company that manufactured the gloves in question. He was responsible for the design, manufacturing, production, raw materials, sales and marketing of all men’s gloves at the company. On the witness stand, when the gloves were shown to him, he identified them as model style 70263 which he said was exclusive to Bloomingdales and that no other company had that model in the United States. According to his testimony, he was able to identify the model because of the “particular type of sewing” which was unique to the model, “the weight of the cashmere lining,” “the weight of the leather utilized,” and “the way the vent was put into the palm.” Mr. Rubin was clear, thorough and unmistakable in the identification of the two gloves and testified that they were indeed a matching pair. For this, P ∗ P ∗ c we set (C3 |C) = 0.98; but just in case he could have been mistaken, we set (C3 |C ) = 0.02.

Next, we consider nodes A, B, and I collectively. Here, we encounter again a scenario where one node (I) has two parents, nodes A and B. This means that our beliefs about the probative force of events at node I on events at node B is not independent of our beliefs about events at node A. In other words, whether the blood found on the right-handed glove matched O.J.’s blood type depends upon whether a right-handed glove was found at O.J.’s residence in the ﬁrst place and upon whether the left-handed glove discovered at the crime scene belongs to O.J. Simpson. With this linkage pattern, we would need to specify the following probabilities: P(I|AB), P(I|AcB), P(I|ABc), P(I|AcBc). Now, if the left hand brown leather glove found at the murder scene belongs to O.J. and a right hand brown leather

52 glove was found at O.J.’s residence, then we suppose that there is a high probability that the blood found on the right hand leather glove matches O.J.’s blood type. We assigned a high value of 0.99 to this probability (P(I|AB)), because this right hand glove was an evidence connected to the murder scene and found at O.J.’s house which was not even the crime scene, coupled with the fact that a left hand of the same glove was located at the crime scene and was believed to belong to O.J. Moreover, in a bloody crime, the assailant tends to leave behind some type of physical evidence such as blood, hair, etc. In this case, the assailant left one hand glove at the crime scene, the matching hand was located at O.J.’s house with blood on it; it is highly likely that this blood would match O.J.’s blood type. Now, if no glove was found at the crime scene but a bloody right hand glove was found at O.J.’s residence, the blood on the glove might still match O.J.’s blood type; so, we have P(I|AcB) = 0.65. On the other hand, if no glove was found at O.J.’s residence but a glove was located at the crime scene, then we believe the probability of this glove belonging to O.J. would be very small nothwithstanding that he was the ex-husband of Nicole. If the left hand glove was not found at the crime scene and the right hand glove was not located at O.J.’s residence but somewhere else, we believe it weakly possible that the blood on the right hand glove would match O.J.’s blood type; so we set P(I|AcBc) = 0.05.

To prove event B (A right-handed brown leather glove was found at O.J. Simpson’s Rockingham residence), we introduced the testimonies of the four Los Angeles county detectives (Vannatter, Lange, Phillips and Fuhrman) who went to O.J. Simpson’s residence in the early hour of the morning of June 13th 1994, supposedly to inform O.J. of the death of his ex-wife. Each one of them testified to the discovery of a right-hand brown leather glove at a remote part of O.J.’s Rockingham residence. Since each one of them testified to exact same event, we decided to aggregate their testimonies and found such testimonies very credible. First, there was no dispute about the existence of a right-handed brown leather glove but the question looms on where it came from, even up to this day! The detectives claimed to have discovered it at O.J.’s Rockingham residence; the defense insinuated that it was picked up at the crime scene by one of the detectives and planted it at O.J’s residence in order to frame him. Such a claim, either direct or insinuated does not fly in the face of other known facts of the case. For example, the detectives did not arrive at the crime scene until about three hours after the first police patrol had arrived at the crime scene, by which

53 time the crime scene had been secured and many other Police Officers were also present. The first Police Officer to arrive at the crime scene was Officer Lance Riske who testified that he only observed one glove (the left hand) at the crime scene which he later showed to the detectives when they arrived about three hours later. Other Police Officers who arrived at the crime scene before the detectives also corroborated the fact that there was only one glove discovered at the crime scene. It is then preposterous and defies logic for anyone to imply that there were two gloves at the crime scene when the first arrivals at the scene only testified to have seen one glove and those who supposed to have taken the right hand glove from the crime scene and planted it at O.J.’s house did not even get to the crime scene until three hours after the first Officer arrived at the scene. To prove event I (The blood found on the right-handed glove matched O.J.’s blood type), we introduced the testimony of Dennis Fung, the Los Angeles Criminalist who testified at the Grand Jury proceedings and also at the Trial that upon laboratory testing, the blood found on the right hand glove matched the blood type of O.J. Simpson, and also that of the two victims - Nicole Brown Simpson and Ronald Goldman. As a trained and certified Criminalist with some years of experience in Forensic analysis, we assigned a very high value to his hit probability; hence we set P(I∗|I) = 0.98. Although we take Dennis Fung to be highly credible in his testimony, we believe his false-positive probability will still be greater than zero because many scientific tests such as that performed by Mr. Fung don’t enjoy a one hundred percent accuracy. But false-positive probabilities are usually small. So, we assigned P(I∗|Ic) = 0.05.

We next consider node D. To prove event D (Nicole Simpson bought two pairs of Aris leather gloves at Bloomingdales in Dec. 1990), we ﬁrst introduced the testimony, D∗, of Ms. Brenda Vemich, and also two other propositions, events G and H. Ms. Vemich was a Sales Associate and gloves buyer in the men’s glove section at Bloomingdales in December 1990. She testiﬁed at the trial, based on the information on the receipt of purchase made at Bloomingdales by Nicole in December of 1990, that Nicole bought two pairs of Aris light leather men’s gloves at the store on December 18, 1990. Given that Nicole bought two pairs of the gloves at Bloomingdales, we suppose it is highly probable that Ms. Vemich would be able to decipher that from the sales receipt based on her experience as a Sales Associate at the store; so we set her hit probability P(D∗|D) = 0.95. Because Ms. Vemich was going by the information on the sales receipt, we believe the chances of her erring in judgement will

54 be very low; and we have her false-positive probability, P(D∗|Dc) = 0.02.

Now we look at nodes D, G, and H collectively where node H has two parents, D and G. As we’ve pointed out in this type of structure, there is conditional dependency between D and G given H. That is, whether or not the gloves found at the murder scene and O.J’s residence were similar to the ones purchased at Bloomingdales by Nicole depends on whether or not Nicole bought two pairs of Aris light leather gloves at Bloomingdales in December of 1990 and also whether or not she gave a pair of gloves to O.J. as present. For this linkage, we need to specify four prior probabilities: P(H|DG), P(H|DGc), P(H|DcG), and P(H|DcGc). For the ﬁrst prior, if Nicole bought a pair of Aris leather gloves at Bloomingdales and gave O.J. a pair as present, we suppose that it is highly probable that the gloves found at the murder scene and O.J.’s residence were similar to the ones purchased at Bloomingdales by Nicole. With this reasoning, we have set P(H|DG) = 0.99. Let us assume that Nicole bought two pairs of Aris leather gloves at Bloomingdales in December 1990 (event D) but she never gave any pair to O.J. as present (event Gc); however, O.J. could still have had access to a pair of the gloves given that they used to be husband and wife leaving under the same roof. As a result, we still feel it is highly probable that the gloves found at the murder scene and O.J.’s residence were similar to the ones purchased at Bloomingdales by Nicole. For this, we assigned a value of 0.80 to P(H|DGc). Next, we considered the intersection of events Dc and G to be null because if Nicole did not purchase the two pairs of gloves at Bloomingdales, she could not have given one pair to O.J. as a present. By the same token, the intersection of events Dc and Gc is also meaningless which renders the events in node H equaly meaningless. Therefore, we have P(H|DcG) = P(H|DcGc) = 0.

To prove event H, the prosecution introduced the testimony of both Ms. Brenda Vemich and Mr. Richard Rubin both of whom testiﬁed that the two gloves (one recovered from the murder scene and the other from O.J.’s residence) were both similar to the gloves purchased by Nicole from Bloomingdales in December 1990. We aggregated the testimonies of these two witnesses and designated them as prosecution testimony as we have in H∗. We have ∗ expressed high level of credence in the testimonies of these two individuals earlier (see C2 ∗ and C3 ) and will still express high level of believability here, though less than before, by P ∗ ∗ ∗ setting (H |H) = 0.85. The assigned probability value here is less than in C2 and C3

55 mainly because of the subject matter of the testimonies: Here, their testimonies were on whether the gloves they were shown were similar to the ones purchased by Nicole while their ∗ ∗ testimonies in C2 and C3 regarded whether a pair of gloves they manufactured and sold were matching pair. If we assume that the gloves found at the murder scene and O.J.’s residence were not similar to the ones purchased at Bloomingdales by Nicole, we set the probability that the witnesses would give this testimony, P(H∗|Hc) = 0.05. This is because we believe that the tendency for the two witnesses to make mistake identifying gloves that are similar is very low given their combined experience in dealing with gloves.

To further prove event H, gloves found at the murder scene and O.J.’s residence were similar to the ones purchased at Bloomingdales by Nicole, we introduced proposition E, the pair of gloves were Aris leather. This is because, for the two sets of gloves to be similar, they all have to be Aris light leather, especially because the recovered gloves have been identiﬁed to be Aris light leather. So, if we suppose that the glove found at the murder scene and O.J.’s residence were similar to the ones purchased at Bloomingdales by Nicole, we set the probability that the pair of gloves were Aris leather, P(E|H) = 0.75 while we set P(E|Hc) = 0.05.

These probability values are presented in Table 4.5 as prior probabilities and are fed into the Hugin software and after conditioning on the evidence nodes (asterisked nodes), we then run the Bayesian network algorithm after which we refer to the network as being compiled. The software then updated the probability values at each of the nodes in light of the evidence. These updated probability values are now the posterior probabilities for ∗ each node; that is, the probabilities conditional on E3 . A table of posterior probabilities P ∗ for each node is displayed in Table 4.6. From the table, we obtained (H5|E3 ) = 0.9890 P c ∗ and (H5|E3 ) = 0.0110 for our network of evidence related to the gloves. Again, using an

∗ appropriate version of equation (4.1), we calculated their ratio to be LE3 = 89.90. This means it is about ninety times as likely to obtain the evidence in this collection if we suppose O.J. Simpson committed the two murders than if we suppose he did not commit the two murders.

List of propositions and evidence items for The Gloves:

1. H5: OJ committed the two murders

56 2. A: A left-handed brown leather glove that belongs to O.J. was found at the crime scene

∗ 3. A1: Oﬃcer Riske’s testimony

∗ 4. A2: Testimony of L.A. detectives to A

5. B: A right-handed brown leather glove was found at O.J.’s Rockingham residence

6. B∗: L.A. detectives testimony to B

7. C: The two gloves are a matching pair

∗ 8. C1 : L.A. detectives testimony to C

∗ 9. C2 : Ms. Vemich’s testimony to C

∗ 10. C3 : Richard Rubin’s testimony to C

11. D: Nicole Simpson bought two pairs of Aris light leather gloves at Bloomingdales in Dec. 1990

12. D∗: Ms. Vemich’s testimony to D

13. E: The pair of gloves were Aris light leather

∗ 14. E1 : Ms. Vemich’s testimony to E

∗ 15. E2 : Mr. Rubin’s testimony to E

16. F: Type of gloves were exclusive to Bloomingdales in the U.S.

∗ 17. F1 : Ms. Vemich’s testimony to F

∗ 18. F2 : Mr. Rubin’s testimony to F

19. G: Nicole gave a pair of gloves to O.J. as present

20. H: Gloves found at the murder scene and O.J.’s residence were similar to those purchased at Bloomingdales by Nicole

21. H∗: Ms. Vemich’s testimony to H

57 22. I: The blood found on the right-handed glove matched O.J.’s bloodtype

23. I∗: Testimony of Dennis Fung, L.A. Police dept. Criminalist

Table 4.5: Prior probabilities for propositions relating to “The Gloves” evidence.

Prob. Values Prob. Values c P(H5) 0.5 P(D|C ) 0.10 P c P ∗ (H5) 0.5 (D |D) 0.95 ∗ c P(A|H5) 0.90 P(D |D ) 0.02 P c P (A|H5) 0.01 (E|H) 0.75 P ∗ P c (A1|A) 0.98 (E|H ) 0.05 P ∗ c P ∗ (A1|A ) 0.01 (E1 |E) 0.95 P ∗ P ∗ c (A2|A) 0.95 (E1 |E ) 0.02 P ∗ c P ∗ (A2|A ) 0.10 (E2 |E) 0.98 P P ∗ c (B|A) 0.80 (E2 |E ) 0.02 P(B|Ac) 0.02 P(F |E) 0.90 P(B∗|B) 0.99 P(F |Ec) 0.01 ∗ c P(B |B ) 0.05 P(F1∗|F ) 0.97 P P ∗ c (C|AB) 0.95 (F1 |F ) 0.02 P c P ∗ (C|AB ) 0.00 (F2 |F ) 0.97 P c P ∗ c (C|A B) 0.00 (F2 |F ) 0.02 P(C|AcBc) 0.00 P(G|D) 0.80 P ∗ P c (C1 |C) 0.65 (G|D ) 0.30 P ∗ c P (C1 |C ) 0.30 (H|DG) 0.99 P ∗ P c (C2 |C) 0.90 (H|DG ) 0.80 P ∗ c P c (C2 |C ) 0.05 (H|D G) 0.00 P ∗ P c c (C3 |C) 0.98 (H|D G ) 0.00 P ∗ c P ∗ (C3 |C ) 0.02 (H |H) 0.85 P(D|C) 0.85 P(H∗|Hc) 0.05 P(I|BA) 0.99 P(I|BcAc) 0.05 P(I|BcA) 0.20 P(I∗|I) 0.98 P(I|BAc) 0.65 P(I∗|Ic) 0.05

58 Table 4.6: Posterior probabilities for propositions relating to “The Gloves” evidence.

Nodes Nodes Prob. Values OJ committed the two murders H5 0.9890 A left-handed brown leather glove was found at the crime scene ... A 1.0000 A right-handed brown leather glove was found at O.J.’s residence B 1.0000 The two gloves were a matching pair C 1.0000 Nicole Simpson bought two pairs of Aris light leather gloves at ... D 1.0000 The pair of gloves are Aris light leather E 1.0000 Type of gloves were exclusive to Bloomingdales in the U.S. F 1.0000 Nicole gave a pair of gloves to O.J. as present G 0.8318 Gloves found at the murder scene and O.J.’s residence were similar ... H 0.9998 The blood found on the right-handed glove matched O.J.’s bloodtype I 0.9995

59 Figure 4.3: A Bayesian Network for “The Gloves” evidence

OJ committed the two murders(H5) The blood found on the right hand glove matched A left-handed brown O.J.’s blood type(I) leather glove found at Officer Riske’s the crime scene testimony(A1*) belongs to OJ(A)

A right-handed brown Testimony of L.A. leather glove was found Detectives(A2*) at O.J.’s Rockingham The two gloves are residence(B) a matching pair© L.A. Detectives Testimony of testimony(C1*) L.A. Detectives Dennis Fung, LAPD testimony(B*) Criminalist(I*) Brenda Vemich’s Nicole Simpson bought two testimony(C2*) pairs of Aris light leather Types of gloves gloves at Bloomingdales in were exclusive to Richard Rubin’s December 1990(D) Bloomingdales in testimony(C3*) The pair of gloves were the U.S.(F) Aris light leather(E) Ms. Vemich’s testimony(D*) Ms. Vemich’s Nicole gave a pair Gloves found at the murder testimony(F1*) of gloves to O.J. scene and O.J.’s residence were similar to the ones purchased as a present(G) Mr. Rubin’s at Bloomingdales by Nicole(H) testimony(E2*)

Prosecution Ms. Vemich’s Mr. Rubin’s testimony(H*) testimony(E1*) testimony(F2*)

60 4.4 The weapon (knife)

∗ This evidence category is labeled “The weapon” denoted as E4 . In several testimonies during the trial, it was revealed by both the law enforcement agents and forensic experts that each of the victims sustained several stab wounds to their bodies including a slash to each of their throats. This led to one logical conclusion that the victims were stabbed to death with what appeared to be a knife, although to this day, the murder weapon was never found. However, there were also testimonies that about thirty days before the murder took place, O.J. Simpson purchased what was described as a stiletto knife from a cutlery store in downtown Los Angeles. This knife was described as having a single-edged blade that can inﬂict cuts similar to those sustained by the victims. All the evidence items related to the purchase of this knife by O.J. Simpson constitute the analysis in this evidence category. With the aid of propositions to connect the gloves evidence items to our main hypothesis, we shall construct a network for this evidence category and evaluate the probative force of the collection of such evidence items. The list of the evidence items and the interim probanda is presented on page 66, the prior probability table is presented in Table 4.7, and the resulting network is presented in Figure 4.4. ∗ led “The weapon” denoted as E4 . In several testimonies during the trial, it was revealed by both the law enforcement agents and forensic experts that each of the victims sustained several stab wounds to their bodies including a slash to each of their throats. This led to one logical conclusion that the victims were stabbed to death with what appeared to be a knife, although to this day, the murder weapon was never found. However, there were also testimonies that about thirty days before the murder took place, O.J. Simpson purchased what was described as a stiletto knife from a cutlery store in downtown Los Angeles. This knife was described as having a single-edged blade that can inﬂict cuts similar to those sustained by the victims. All the evidence items related to the purchase of this knife by O.J. Simpson constitute the analysis in this evidence category. With the aid of propositions to connect the gloves evidence items to our main hypothesis, we shall construct a network for this evidence category and evaluate the probative force of the collection of such evidence items. The list of the evidence items and the interim probanda is presented on page 66, the prior probability table is presented in Table 4.7, and the resulting network is presented in Figure 4.4.

61 For this evidence category, we have nineteen nodes with connecting links and about forty-two prior probability ingredients. We start with our usual root node consisting of our c P main hypothesis H5 and its complement H5. We begin in our usual way by setting (H5) P c = (H5) = 0.5. As we have done with the other networks, we shall explain our rationale for the specific arrangement of the nodes in this particular network and the assigned prior probabilities. Many of the probability values were intuitively assigned; for those, not much explanation will be provided. However, there are those where detailed explanations will be provided to expose the evidential subtleties present in them. As indicated in the beginning, we know the victims were stabbed to death and there were testimonies to the effect that O.J. purchased a stiletto knife. We begin with the following line of reasoning: if O.J. committed the murders (node H5), then he probably committed the murders with a stiletto knife (node A). But we also know that even if he purchased a stiletto knife, he could have killed the victims with a different knife, not necessarily a stiletto; with this in mind we assigned a very low probability of 0.2 to P(A|H5). Now, if we assume O.J. did not commit the murders, then he could not have killed them with a stiletto knife, meaning that the intersection of events c P c A and H5) does not exist; in that case, (A|H5) = 0 automatically.

To prove proposition A, we introduced two lines of argument: event B, that the stiletto knife purchased by O.J. was the same type of knife used to kill both NBS and RLG, and event C, O.J. intended to kill NBS with a knife. First with event B, we suppose that if O.J. committed the murders with a stiletto knife (node A), then the stiletto knife purchased by O.J. was the same type of knife used to kill both NBS and RLG (node B). We assigned 0.95 to P(B|A). But if O.J. did not commit the murders with a stiletto knife then P(B|Ac) becomes meaningless and we assigned a value of zero to that probability. In node H, we believe that it is eight times more likely that the stiletto knife purchsed by O.J. was a single- edged blade, if we suppose that the stiletto knife purchased by O.J. was the same type used to kill NBS and RLG than if we suppose it was not. So, we have set P(H|B) = 0.80 and P(H|Bc) = 0.10. To prove H we introduced the testimony of Mr. Camacho who was one of the salesmen at Ross Cutlery store in downtown Los Angeles where O.J. allegedly purchased a stiletto knife who testiﬁed, among other things, that the knife purchased by O.J. was a single-edged knife. We gave his hit probability a very high value and set P(H∗|H) = 0.98

62 and P(H∗|Hc) = 0.01. Here we have a strong belief that as a sales person at a cutlery store, Mr. Camacho would have no problem identifying a single-edged blade; for this, we assigned a very low value (0.01) to his false-positive probability.

We also introduced one line of argument to prove H: event I, that the wounds sustained by the victims were consistent with injuries inflicted by a single-edged blade; so we linked node H with node I. We suppose that it is highly probable that if the knife purchased by O.J. Simpson was a single-edged blade, then the wounds sustained by the victims were consistent with injuries inflicted by a single-edged blade; so we set P(I|H) = 0.92. Suppose the knife purchased by O.J. was not a single-edged blade, say a double-edged blade; it is still barely possible that the wounds sustained by the victims were consistent with injuries inflicted by a single-edged blade. It could be because of the angle of entry of the knife into the victims’ bodies or because O.J. used a knife different from the one he purchased; so, we set P(I|Hc) = 0.02. Dr. Irwin Golden, the Deputy Medical Examiner at the Los Angeles County Department of the Coroner, testified during the Grand Jury proceedings and the preliminary hearing that the wounds sustained by the victims were consistent with injuries inflicted by a single-edged blade. This testimony we used to prove that the event I is true. As a licensed physician with about fourteen years experience working at the Coroner office, we give his testimony a very high credibility; for this we assigned a high value of 0.96 to his hit probability, P(I∗|I) and assigned a very low value (0.02) to his false-positive probability, P(I∗|Ic).

To prove event C (O.J. intended to kill NBS with a knife), we introduced four lines of argument: (1) event F , Both NBS and RLG sustained a slash to the throat, (2) event G, NBS and RLG sustained multiple stab wounds, (3) event D, O.J. purchased a stiletto knife from a cutlery store, and (4) event E, O.J. requested a knife sharpened at the cutlery store. In addition to proving event C, event E is also used to prove event D giving node E two parents, node C and node D. One of the easiest ways to kill another person is to slash the throat, cutting through the jugular veins; so, a slash in the throat must have been preceeded by an intent to take the life; and the act itself is in furtherance of the intent to kill. With this in mind, we believe it is forty times more likely that the victims were slashed in the throat (node F ) if we suppose O.J. intended to kill NBS with a knife (node C) than if we suppose

63 he did not. For this, we have set P(F |C) = 0.80 and P(F |Cc) = 0.02. We also believe that it is sixteen times more likely that NBS and RLG sustained multiple stab wounds (node G) if we suppose O.J. intended to kill NBS with a knife (C)than if we suppose he did not. Here, we set P(G|C) = 0.80 and P(G|Cc) = 0.05. If one intends to kill another person with a knife, a logical step would be to procure the knife if one doesn’t have it yet; so, we believe it is highly probable that O.J. purchased a stiletto knife from a cutlery store (node D) given that he intended to kill NBS with a knife (C) and we assign a probability value of 0.95 to P(D|C). Now, if we suppose O.J. did not intend to kill NBS with a knife (Cc), it is still possible that he might have gone out to buy a stiletto knife; perhaps because he collects knives as a hobby or he needed a knife for some legitimate household use. In this instance, we assigned a substantial value of 0.25 to P(D|Cc).

In node E, we encounter again a situation where a node, E, has two parents or sources of probabilistic inﬂuence, nodes C and D. In other words, our belief about the probative force of events at node E on events at node D is not independent of events at node C. That is to say that whether O.J. requested a knife to be sharpened at the cutlery store depends on whether he purchased a knife from the cutlery store and also depends on what his intentions were when he purchased the knife. With this type of linkage structure, we are required to provide four prior probability values: P(E|CD), P(E|DCc), P(E|DcC), and P(E|DcCc). Now, if O.J. intended to kill NBS with a knife (node C) and in furtherance of his intent, purchased a stiletto knife from a cutlery store (node D), then we believe it highly likely that he requested a knife sharpened at the cutlery store (node E) in order to increase the likelihood of achieving his objective; so we set P(E|CD) = 0.95. However, if he did not intend to kill NBS with a knife (event Cc) but purchased a stiletto knife for other reasons, the probability may still be high that he requested a knife sharpened at the cutlery store (event E); so we set P(E|DCc) = 0.70. On the contrary, if O.J. intended to kill NBS with a knife but did not purchase a stiletto knife at a cutlery store, he might have decided to use a knife he already had at home, perhaps received as a gift; and he might still have requested this knife sharpened at a cutlery store. Although it is not a common occurence for someone to just walk into a cutlery store without any purchase and asked that a knife be sharpened for him, we acknowledge that it is not an impossible event either (especially if one was determined to kill), but one with a low probability; so we set P(E|DcC) = 0.15.

64 Finally, without any intention to kill and with no purchase of a knife at a cutlery store, it is highly unlikely that O.J. would go to a cutlery store and requested a knife be sharpened; so, we assigned P(E|DcCc) a very low value of 0.02.

We use Mr. Jose Camacho’s testimony to further prove event D and also as a proof of event E. In the Grand Jury proceedings and preliminary hearings, Camacho testified that O.J. Simpson came to the cutlery store where he worked as a sales person, purchased a single-edged stiletto knife, and requested that the knife be sharpened. We have no reason to doubt his testimony, at least not to any significant degree. As a result, we have set P(D∗|D)= P(E∗|E) = 0.98. Although we have confidence in the veracity of Mr. Camacho’s testimony, we acknowledge that as a human being, he could possibly be mistaken, not in what transpired at the store but in the identification of O.J. Simpson. The probability of the mistaken identity, we believe it’s pretty small given the celebrity status of O.J. Simpson, not only in the entire country but especially in the Los Angeles area where the cutlery store was located. With this in mind, we set P(D∗|Dc) = P(E∗|Ec) = 0.001.

To prove events F (Both NBS and RLG sustained a slash to the throat) and G (NBS and RLG sustained multiple stab wounds), we introduced the testimony of Dr. Irwin Golden, the deputy medical examiner at the L.A county Coroner’s office. He testified that both victims were slashed at the throat and also sustained multiple stab wounds all over their bodies. This testimony was also corroborated by the police officers and the detectives who responded to the crime scene. We aggregated the testimonies of the medical examiner and the law enforcement officers as F ∗ to prove F and as G∗ to prove G and find them credible. So, we set P(F ∗|F ) = P(G∗|G) = 0.99 and P(F ∗|F c) = P(G∗|Gc) = 0.02. To further prove both events F and G, we introduced a line of argument: event J, both NBS and RLG died as a result of injuries sustained from the attack of the evening of June 12th 1994 which gives node J, two parents, nodes F and G. A slash of the throat in and of itself is an injury fatal enough to result in death, so are multiple stab wounds or combination of both. So, if the victims were slashed at the throat (event F ) and, in addition, both sustained multiple stab wounds (event G), we suppose that the probability is almost one that they both died from the attack. With this line of reasoning, we set P(J|GF ) = 0.999. Even if the victims were not slashed at the throat (event F c) but sustained multiple wounds (event G), we believe it is still

65 highly probable that the victims died from the attack. So, we assigned a probability value of 0.70 to P(J|GF c). If we consider the possibility of the victims only sustained slashes to the throat (event F ) but did not sustain multiple stab wounds (event Gc), as indicated above, a slash to the throat is a fatal injury with a potential deadly consequence even without any additional injuries. We then suppose that it is highly probable that the victims died from this attack; hence we have P(J|GcF ) = 0.95. We assigned a very low probability to P(J|GcF c) and gave it a value of 0.02, reflecting our belief that the victims might still have died from the attacks of the evening of June 12th, 1994 even without slashes to the throat or multiple stab wounds all over their bodies. A mere sight of, or struggle with an assailant could have led to a cardiac arrest or some other type of life-threatening medical complications. To prove event J, that both NBS and RLG died from injuries sustained from the attack of the evening of June 12th 1994, we introduced the testimony of Dr. Irwin Golden, the deputy medical examiner at the Los Angeles county Coroner’s office who conducted autopsy on the bodies of the two victims. He testified during Grand Jury proceedings and Trial that the two victims sustained slashes to the throat and multiple stab wounds and concluded in his expert opinion that they both died from those injuries. We judged this testimony to be highly reliable and set his hit probability, P(J ∗|J) = 0.99 and his false-positive probability, P(J ∗|J c) = 0.001.

To calculate the likelihood ratio for evidence in this category, we need the posterior probabilities for our main hypothesis node which can be obtained from the compiled Bayesian P ∗ network. For our network of evidence related to the purchased knife, (H5|E4 ) = 0.9919,

P c ∗ ∗ (H5|E4 ) = 0.0081, and their ratio, LE4 = 122.5. This means it is about one hundred and twenty three times as likely to obtain the evidence in this collection if we suppose O.J. Simpson committed the two murders than if we suppose he did not.

List of propositions and evidence items for The Weapon (knife):

1. H5: OJ committed the two murders

2. A: OJ committed the two murders with a stiletto knife

3. B: The stiletto knife purchased by OJ was the same type of knife used to kill both NBS and RLG

66 4. B∗: Expert testimony to B

5. C: OJ intended to kill NBS with a knife

6. D: OJ purchased a stiletto knife from a cutlery store

7. D∗: Camacho’s testimony to D

8. E: OJ requested a knife sharpened at the cutlery store

9. E∗: Camacho’s testimony to E

10. F: Both NBS and RLG sustained a slash to the throat

11. F ∗: Expert/Police testimony to F

12. G: NBS and RLG sustained multiple stab wounds

13. G∗: Expert testimony to G

14. H: The stiletto knife purchased by O.J. was a single-edged blade

15. H∗: Camacho’s testimony to H

16. I: Wounds sustained by the victims were consistent with injuries inﬂicted by a single- edged blade

17. I∗: Expert testimony to I

18. J: Both NBS and RLG died as a result of injuries sustained from the attack of the evening of June 12th 1994

19. J ∗: Expert testimony to J

67 Table 4.7: Prior probabilities for propositions relating to “The Weapon” evidence.

Prob. Values Prob. Values ∗ P(H5) 0.50 P(E |E) 0.98 P c P ∗ c (H5) 0.50 (E |E ) 0.001 P(A|H5) 0.20 P(F |C) 0.80 P c P c (A|H5) 0.00 (F |C ) 0.02 P(B|A) 0.95 P(F ∗|F ) 0.99 P(B|Ac) 0.00 P(F ∗|F c) 0.02 P(B∗|B) 0.95 P(G|C) 0.80 P(B∗|Bc) 0.20 P(G|Cc) 0.05 P(C|A) 0.85 P(G∗|G) 0.99 P(C|Ac) 0.05 P(G∗|Gc) 0.02 P(D|C) 0.95 P(H|B) 0.80 P(D|Cc) 0.25 P(H|Bc) 0.10 P(E|DC) 0.95 P(H∗|H) 0.98 P(E|DCc) 0.70 P(H∗|Hc) 0.01 P(E|DcC) 0.15 P(I|H) 0.92 P(E|DcCc) 0.02 P(I|Hc) 0.02 P(I∗|I) 0.96 P(I∗|Ic) 0.02 P(J|GF ) 0.999 P(J|GF c) 0.75 P(J|GcF ) 0.95 P(J|GcF c) 0.02 P(J ∗|J) 0.99 P(J ∗|J c) 0.001 P(D∗|D) 0.98 P(D∗|Dc) 0.001

Table 4.8: Posterior probabilities for propositions relating to “The Weapon” evidence.

Nodes Nodes Prob. Values OJ committed the two murders H5 0.9919 OJ committed the two murders with a stiletto knife A 0.9854 The stiletto knife purchased by OJ was the same type of knife used ... B 0.9840 OJ intended to kill NBS with a knife C 0.9997 OJ purchased a stiletto knife from a cutlery store D 1.0000 OJ requested the knife sharpened at the cutlery store E 0.9999 Both NBS and RLG sustained a slash to the throat F 0.9961 NBS and RLG sustained multiple stab wounds G 0.9952 The knife purchased by O.J. was a single-edged blade H 1.0000 Wounds sustained by the victims were consistent ... single-edged blade I 0.9982 Both NBS and RLG died as a result of injuries sustained from ... J 1.0000

68 Figure 4.4: A Bayesian Network for “The Weapon” evidence

OJ committed the two murders(H5)

OJ committed the two murders with a stiletto knife(A)

The stiletto knife purchased by OJ was the OJ intended to kill OJ requested a knife same type of knife used to NBS with a knife© sharpened at the kill both NBS and RLG(B) cutlery store(E)

Expert Both NBS and RLG OJ purchased a testimony(B*) sustained a slash to stiletto knife from a cutlery store(D) The stiletto knife the throat(F) purchased by OJ was a Camacho’s single-edged blade(H) NBS and RLG testimony(E*) sustained multiple Expert/Police stab wounds(G) testimony(F*) Wounds sustained by the Camacho’s victims were consistent testimony(D*) with those inflicted by a single-edged blade(I) Expert/Police Camacho’s testimony(G*) testimony(H*) Both NBS and RLG died from the injuries sustained Expert from the attack on the testimony(I*) evening of June 12th 1994(J) Expert testimony(J*)

69 4.5 Knowledge of Guilt

∗ This evidence segment is labelled “Knowledge of guilt” and denoted as E5 . In most criminal cases, the perpetrator usually leaves behind some evidence; sometimes, it’s physical such as clothing, footprints, ﬁngerprints, blood specimen, etc. At other times, the evidence is psychological such as action or inaction on the part of the perpetrator after a criminal act; for example, a perpetrator of a crime has the tendency to ﬂee the crime scene. In this evidence sector, we shall collect all the psychological evidence pointing to the fact that O.J. Simpson was well aware of the fact that he had committed murder, a criminal act, and some of his actions that were consistent with someone who committed such an act. With the aid of propositions to suggest his knowledge of guilt, we shall construct a network for this evidence category and evaluate the probative force of the collection of such evidence items. The list of the evidence items and the interim probanda is presented on page 73, the prior probability table is presented in Table 4.9, and the resulting network is presented in Figure 4.5. The network consists of twelve nodes connected by links. As usual, at the top of the network is the node representing the penultimate probandum PP5 (O.J. committed ∗ ∗ ∗ the two murders) denoted as H5 while the evidence nodes (D , G , H ) are at the bottom ∗ of the network. The evidence subset E5 is the conjunction of these evidence nodes; that ∗ ∗ ∗ ∗ is, E5 = D ∩ G ∩ H . These evidence nodes are connected to H5 by arrays of interim probanda (or hypotheses) representing several stages of reasoning. Each link in the chain of reasoning exposes a source of doubt concerning the probative strength of the evidence on H5.

As we have done with all of the networks, we assigned a noninformative prior of 0.5 each to our main hypothesis and its complement at the top node. To prove H5, our main hypothesis, we introduced proposition A, O.J. was conscious of being the assailant in the commission of a murder.We believe that if O.J. committed the murders, he must be conscious of being the assailant in the commission of a murder, with a high probability. With this line of reasoning, we have set P(A|H5) = 0.99; although extremely unlikely, we feel it is still humanly possible for O.J. Simpson to have committed the murders and not be conscious of P c it afterwards. We then have (A|H5) = 0.02 because we feel it’s most unlikely for O.J. to be conscious of being the assailant in the commission of murders that he did not commit. To prove event A, we introduced node B, right below node A, where we have the proposition

70 that if O.J. Simpson was conscious of having committed the murders, he must be conscious of having committed a criminal act (event B), with certainty; therefore we have set P(B|A) = 1.00. We can not believe that O.J. Simpson did not know that killing two people is a criminal act. But we have P(B|Ac) = 0.05, the probability that O.J. was conscious of committing a criminal act, given that he was not conscious of being the assailant in the commission of a murder. In this case, he could have been conscious of a diﬀerent criminal act, other than the killing of Nicole and Ron Goldman. Naturally, when someone commits a criminal act, he or she usually wants to escape from the law; so we suppose that if O.J. was conscious of having committed a criminal act, then he would want to escape from the justice system. As a result, we set P(C|B) = 0.80, but set P(C|Bc) = 0.02 because if O.J. was not conscious of having committed a criminal act, he most probably had nothing to do with it and would have no reason to want to escape from the law.

To prove node C, it is directly linked to three different nodes (D, E, and F ). If we suppose that O.J. wanted to escape from the law, it would make sense that he wouldn’t want to turn himself in to the law enforcement authority (node D), even if he was required to do so as evident from the infamous white Bronco chase that lasted for several hours on a Los Angeles freeway; we assigned a very high probability of 0.98 to this proposition (P(D|C)). On the other hand, if he was not trying to escape from the law, perhaps had the intention of turning himself in but riding around in the white Bronco for a different reason; or he might just be disoriented from side effects of some medication or other sources. As a result, we have P(D|Cc) = 0.05. The next node directly linked to node C is node F where we have the proposition that O.J. wanted to take his own life, given that he wanted to escape from the law. It is a fairly common phenomenon that those who are accused of committing a serious crime or/and actually committed the crime try to kill themselves as one way of escaping from the law. In this case, we consider this somewhat probable, especially if we give credence to the testimony of O.J. Simpson’s close friend, A.C. Cowlings who was in the white Ford Bronco with him. For this node, we have P(F |C) = 0.75. Because of his well known upbeat personality, we do not believe that O.J. would entertain committing suicide if he wasn’t trying to escape from the law, so we set P(F |Cc) = 0.01, assigning that possibility, a very low probability. The last node we offer as a proof for node C is node E. Here, we suppose that if O.J. wanted to escape from the law, one other possibility of achieving that

71 was to run away from the country; so, we have P(E|C) = 0.90. However, if he wasn’t trying to escape from the law, we do not think there would be a reason for him to want to run away from the country; hence we have P(E|Cc) = 0.01. We believe that any accused who wants to run away from the country in order to avoid the law would do his homework and acquire all he needs in order to make a successful getaway. For this reason, we have P(G|E) = 0.90; on the other hand, if there is no intention to run away, there won’t be any need to assemble any getaway kit. Hence we set P(G|Ec) = 0.01.

The prosecution testimony was that during the white Bronco chase that lasted for several hours on a California freeway, O.J. had with him in the vehicle, his passport, a disguise, and ten thousand dollars cash. This evidence, if true, will support the proposition that O.J. had what he needed to escape and money to sustain him in the white Bronco. We put a lot of credibility in this evidence and assigned a high probability of 0.98 (P(G∗|G)) to it; we do not think that the prosecution manufactured this evidence and ﬁnd such falsiﬁcation highly unlikely with a probability of 0.01 (P(G∗|Gc)). One way people commit suicide is to put a gun to their heads and pull the trigger. We suppose that if O.J. wanted to take his life (node F ), he probably put a gun to his head and contemplated pulling the trigger, although we recognize that not everyone commits suicide by shooting themselves in the head. However, considering the statement by A.C. Cowlings, O.J. Simpson’s friend who was riding with him in the white Ford Bronco during the freeway chase, we consider it highly probable that O.J. put a gun to his head and threatened to shoot (node H). In this case, we have P(H|F ) = 0.95; but just in case O.J. was just doing that in jest or he held a fake gun to his head and he did not want to take his life, we set P(H|F c) = 0.01. We put a lot of credibility in A.C. Cowlings’ statement that O.J. had a gun to his head and was threatening to shoot himself, given the circumstances under which A.C. Cowlings made that statement. He made the statement during the white Bronco chase when there were several police cars riding behind the white Bronco in order to alert the police to the extreme danger at hand so that they could pull back the pressure in order to dissuade O.J. from making good on the threat. With this in mind, we have P(H∗|H) = 0.98. We do not believe that A.C. Cowlings would make that statement without such an event happening; therefore we assigned a very low probability of 0.01 to P(H∗|Hc), the probability that A.C. Cowlings made that statement given that O.J. had not put a gun to his head and threatened to shoot.

72 These probability values are presented in Table 4.9 as prior probabilities and are fed into the Hugin software and after conditioning on the evidence nodes (D∗, G∗, and H∗), we then run the Bayesian network algorithm after which we refer to the network as being compiled. The software then updated the probability values at each of the nodes in light of the evidence. These updated probability values are now the posterior probabilities for ∗ each node; that is, the probabilities conditional on E5 . A table of posterior probabilities P ∗ for each node is displayed in Table 4.10. From the table, we obtained (H5|E5 ) = 0.9210 P c ∗ and (H5|E5 ) = 0.0790 for our network of evidence related to knowledge of guilt. Using an

∗ appropriate version of equation (4.1), we calculated their ratio to be LE5 = 12.25. This means it is about twelve times as likely to obtain the evidence in this collection if we suppose O.J. Simpson committed the two murders than if we suppose he did not commit the two murders.

List of propositions and evidence items for Knowledge of guilt:

1. H5: OJ committed the two murders

2. A: OJ was conscious of being the assailant in the commission of a murder

3. B: OJ was conscious of having committed a major criminal act

4. C: OJ wanted to escape from the justice system

5. D: OJ did not intend to turn himself in at the LAPD precinct

6. D∗: The infamous white Bronco chase

7. E: OJ intended to run away from the country

8. F: OJ wanted to take his own life

9. G: OJ had what he needed to escape and money to sustain him in the white Bronco

10. G∗: Police Testimony to G

11. H: OJ put a gun to his head and threatened to shoot

12. H∗: A.C. Cowlings statement

73 Table 4.9: Prior probabilities for propositions relating to O.J. Simpson’s Knowledge of Guilt.

Prob. Values Prob. Values P(H5) 0.5 P(E|C) 0.90 P c P c (H5) 0.5 (E|C ) 0.01 P(A|H5) 0.99 P(F |C) 0.75 P c P c (A|H5) 0.02 (F |C ) 0.01 P(B|A) 1.00 P(G|E) 0.95 P(B|Ac) 0.05 P(G|Ec) 0.02 P(C|B) 0.80 P(G∗|G) 0.98 P(C|Bc) 0.01 P(G∗|Gc) 0.05 P(D|C) 0.98 P(H|F ) 0.95 P(D|Cc) 0.05 P(H|F c) 0.01 P(D∗|D) 0.99 P(H∗|H) 0.98 P(D∗|Dc) 0.01 P(H∗|Hc) 0.01

Table 4.10: Posterior probabilities for propositions relating to O.J. Simpson’s Knowledge of Guilt.

Nodes Nodes Prob. Values O.J. Committed the two murders H5 0.9245 O.J. was conscious of being the assailant .... murder A 0.9426 O.J. was conscious of having committed a major criminal act B 0.9888 O.J. wanted to escape from the justice system C 0.9997 O.J. did not intend to turn himself in at LAPD precinct D 0.9997 OJ intended to run away from the country E 0.9916 O.J. wanted to take his own life F 0.9928 OJ had what he needed to escape and money to sustain .... Bronco G 0.9914 OJ put a gun to his head and threatened to shoot H 0.9958

74 Figure 4.5: A Bayesian Network for Knowledge of Guilt

OJ committed the two murders (H5)

OJ was conscious of being the assailant in the commission of a murder (A)

OJ was conscious of having committed a major criminal act (B)

OJ wanted to escape from the Justice system © OJ did not intend to turn himself in at the LAPD OJ wanted OJ put a gun to precinct (D) to take his his head and own life (F) threatened to shoot (H) A.C. Cowlings’ testimony (H*) OJ intended to The infamous run away from OJ had what he needed white Bronco the country (E) to escape and money Police chase (D*) to sustain him in white testimony Bronco (G) (G*)

75 4.6 Blood Stains

∗ This evidence category is labelled as “Blood stains” and denoted as E6 . As explained in the “Knowledge of guilt” section above, criminals tend to leave some type of evidence behind at the crime scene. In the section above, we analyzed the psychological evidence; in this section, we examine the physical evidence - speciﬁcally, the blood stains. In this case, blood evidence was collected from three main sources: the Bundy crime scene, the O.J.’s Rockingham residence and his Ford Bronco. Using all of the blood evidence collected from these sources, we constructed a Bayesian network for this evidence category and conducted the analysis. At the crime scene, both victims were discovered lying in a pool of their own blood but there were blood stains at a few other spots at the crime scene that were not consistent with either of the two victims. For example, there were bloody shoe prints leading out of the courtyard through the back of the property; there was also a trail of blood drops to the left of the shoe prints. In addition, blood stains were discovered on the rear gate of the property. All of these items, the shoe prints, the drops and the stains by the gate were consistent with the O.J. Simpson DNA proﬁle.

There were several blood stains found in both the interior and the exterior of O.J.’s Ford Bronco. First, there were blood stains on the exterior door handle and the interior of the door of the Driver side of the Bronco. Those stains matched O.J.’s DNA profile. There was a blood stain on the Driver side carpet that matched both Nicole’s and O.J. Simpson’s DNA profiles. On the center console were three blood stains, each of which matched the DNA profile of the two victims, Nicole Simpson and Ron Goldman, and also that of O.J. Simpson. There were two more blood drops on the center console, one of which matched Nicole’s DNA profile, while the other matched both Nicole’s and O.J.’s DNA profiles. Also on the steering wheel was a bloodstain that matched both Nicole’s and O.J.’s DNA profiles.

At O.J.’s Rockingham residence, blood evidence was collected at several locations. First, a right hand glove was found that was soaked in blood. Blood stains were removed from different spots on both the inside and outside of the glove. When the stains were tested, some stains matched Ron Goldman’s DNA profile only, some matched both victims’ DNA profiles only while there were other stains that matched the DNA profiles of both victims

76 and O.J. Simpson. At Rockingham, there were blood trails that led from the Bronco that was parked outside to the gate of the residence. Other blood stains were found at the foyer of the residence and on the floor of the master bedroom. All of these stains matched the DNA profile of O.J. Simpson. Furthermore, a sock was discovered on the floor of the master bedroom with blood stains that matched both O.J.’s and Nicole’s DNA profiles.

A good summary of all the results of the blood tests in the O.J. Simpson case can be found in a paper by William Thompson titled “DNA Evidence in the O.J. Simpson Trial” (see [8], pg. 828 - 829). William Thompson was a member of the Simpson defense team and is currently a Professor at the Department of Criminology, Law and Society at the University of California, Irvine. A similar summary, though in tabular form, can be found in a paper by Bruce Weir titled “DNA statistics in the Simpson matter” (see [9], pg. 366). Bruce Weir was one of the experts who testified for the prosecution at the trial and is currently the Chair of the Biostatistics department at the University of Washington in Seattle. The analysis in this evidence category is based on the results from the summary tables in Weir’s paper which are reproduced in Figure 4.6 below. In the tables, “NB” is used for Nicole Simpson, “OS” for O.J. Simpson, and “RG” for Ron Goldman. Also, “RFLP” stands for Restriction Fragment Length Polymorphisms while “PCR” stands for Polymerase Chain Reaction”; they are both scientific methods used to amplify smaller quantities of DNA into quantities that are large enough for analysis. In Figure 4.6, there was a table created for the blood stains from Simpson’s Rockingham residence, a table for the blood stains collected from the glove recovered from the residence, a table for the stains from the sock recovered from the master bedroom at O.J. Simpson’s residence, a table for all the blood stains from the Ford Bronco and finally, a table for the blood stains at the Bundy crime scene.

The DNA testing in this case was performed by three diﬀerent agencies namely the Los Angeles Police Department (LAPD), the California Department of Justice DNA Laboratory (DOJ) and Cellmark Diagnostics (CMD), a private company located in Gaithersburg, Maryland (see [9], pg. 365). The Thompson summary was based, in part, on laboratory reports prepared by these three agencies and also the testimonies of criminalist, Gary Sims of DOJ and Dr. Robin Cotton, the Lab Director at Cellmark Diagnostics (see [8], footnote 2). The use of duplicate testing in the O.J. Simpson case greatly reduces concerns about the

77 potential for false positive results due to poor scientific practices of DNA laboratories, so argued Thompson (see [8], pg. 827). The testing is based on detecting genetic identification marks carried by each individual referred to as alleles. Each person has two identifying alleles, with one inherited from the father and the other from the mother. The alleles are represented either by numbers or letters depending on the genetic testing system. For example, under the DQ-Alpha system which was frequently referred to in the case, the possible alleles are 1.1, 1.2, 1.3, 2, 3, and 4, while under the LDLR system, the possible alleles are A and B. For a summary of different genetic systems and the possible alleles under each system, see [8], pg. 852, Table 1. Under the DQ-Alpha system, O.J. Simpson’s profile is [1.1, 1.2]; Nicole Simpson’s profile is [1.1, 1.1] - note that it is possible to inherit the same type of allele from each parent as we see here with Nicole; finally, Ron Goldman’s profile is [1.3, 4].

For our network for this category of evidence, the prior probabilities are displayed in Table 4.11 and the posterior probabilities are displayed in Table 4.12. In the posterior probabilities table, we have displayed values to four decimal places for convenience and consistency with the rest of the posterior probability tables, but we actually used more decimal places in our likelihood ratio calculation. After running the default algorithm, we obtained posterior probabilities from which we calculated the likelihood ratio for this category of evidence which turns out to be about 131,120 - a very high value indeed. The reasoning processes in our prior probability assignments in this network are very similar to many of our previous networks, so we will not go through the details of every probability assignment. However, we will explain some of the more important ones. As we’ve done with all of the networks, we assigned a noninformative prior of 0.5 each to our main hypothesis and its complement at the top node. To prove H5, our main hypothesis, we introduced three main propositions: node A, O.J.’s blood was found at the murder scene; node B, the blood of both victims and O.J.’s blood was found in his Ford Bronco; and node C, the blood of both victims and O.J.’s blood was found at O.J.’s Rockingham residence. All of the remaining nodes in the network are hung below these three nodes.

To prove B, we introduced two nodes: node U, Someone with O.J.’s blood type bled in O.J.’s Ford Bronco; and node V , Blood matching both victims’ blood types was found in O.J.’s Ford Bronco. We ﬁrst consider P(U|B), the probability that someone with O.J.’s

78 blood type bled in the Ford Bronco, given that the blood of both victims and O.J.’s blood was found in his Ford Bronco. At first, this conditional probability appeared to be 1.00 but then we considered that the mere fact that O.J.’s blood was found in the Bronco does not necessarily mean that someone with O.J.’s blood type bled in the Bronco; it could also mean that someone intentionally and maliciously planted his blood in the vehicle to frame him, although we believe that possibility to be very remote. Given this reasoning, we have P(U|B) = 0.98. Next is P(U|Bc), the probability that someone with O.J.’s blood type bled in the Bronco, given that it is not true that the blood of O.J. and both victims was found in the Bronco. While on the witness stand, Colin Yamauchi, the LAPD criminalist who testified for the Prosecution, informed the court that, based on the standard statistical tables used and accepted in the field of forensic science, about 7 percent of the population have the same DNA profile as O.J. Simpson, 5 percent have the same DNA profile as Ron Goldman, and 3 percent have the same DNA profile as Nicole Simpson. We interpret P(U|Bc) as the probability that a random person who happened to have the same DNA profile as O.J. bled in the Ford Bronco given that O.J. himself did not bleed in the Bronco. With this explanation, we set P(U|Bc) = 0.07 which is the percentage of the population having the same DNA profile as O.J. Simpson. Next is P(V |B), the probability that blood matching both victims’ blood types was found in O.J.’s Ford Bronco given that the blood of both victims and O.J.’s blood was found in his Ford Bronco. We consider V a certain event conditional on event B and we set P(V |B) = 1.00. We now consider the event V given the complement of B; i.e, given that it is not true that the blood of O.J. and both victims was found in the Bronco, what is the probability that the blood will match both victims’ blood types? We take this to be the probability that the blood belongs to a random person with the same blood type as Nicole and another random person with the same blood type as Ron Goldman. Given that 0.03 of the population have the same blood type as Nicole and 0.05 of the population have the same blood type as Ron Goldman, we take the product of the two numbers, assuming independence, and set P(V |Bc) = 0.0015. To prove C, the blood of both victims and O.J.’s blood was found at O.J.’s Rockingham residence, we introduced two other nodes: W , Someone with O.J.’s blood type bled at O.J.’s Rockingham residence; and X, Blood matching both victims’ blood types was found at OJ’s Rockingham residence. Using the same line of reasoning as in P(U|B) and P(U|Bc), we set P(W |C) = 0.98 and P(W |Cc) = 0.07. Similarly, using the same line of reasoning as in P(V |B) and P(V |Bc), we

79 set P(V |B) = 1.00 and P(V |Bc) = 0.0015.

Now we consider prior probabilities for the evidence nodes; this will mean the “hit” probabilities and “false positive” probabilities of the lab results. In node J, we have the proposition “Blood on the driver side exterior door handle of the Bronco matched OJ’s DNA proﬁle” and node J ∗ contains the event “lab results supporting J”. Acknowledging the fact that a lab can be riddled with mistakes in myriad of ways such as contamination, poor handling, and others, we believe the accuracy of the DNA testing procedure is still very high, in the neighborhood of 98 percent or more. With this in mind, we set the hit probability, P(J ∗|J) =0.98. We know that avoiding mistakes totally in DNA testing is virtually impossible, we believe that the probability of mistakes occurring is very low. Therefore, we set the false positive probability, P(J ∗|J) = 0.02. We used the same hit and false probability values (0.98 and 0.02) used in node J for all the remaining evidence (asterisked) nodes involving lab results such as J ∗, K∗, etc. The remaining prior probabilities assignments can be seen in Table 4.11.

List of propositions and evidence items for Blood Stains

1. H5: O.J. committed the two murders

2. A: O.J.’s blood was found at the murder scene

3. B: The blood of both victims and O.J.’s blood was found on his Ford Bronco

4. C: The blood of both victims and O.J.’s blood was found at O.J.’s Rockingham residence

5. D: Blood stains found on the back gate of NBS house matched O.J.’s DNA proﬁle

6. D∗: Lab results supporting D

7. E: Bloody shoe prints found at the crime scene matched O.J.’s DNA proﬁle

8. F: Bloody shoe prints at the crime scene came from Bruno Magli shoes

9. F ∗: Expert testimony

80 10. G: O.J. owns a pair of Bruno Magli shoes

11. G∗: Prosecution testimony

12. H: Blood drops to the left of shoe prints found at crime scene matched O.J.’s DNA proﬁle

13. H∗: Lab results supporting H

14. I: O.J. had a cut on his left ﬁnger

15. I∗: Detective Vannatter’s testimony

16. J: Blood on the driver side of the exterior door handle of the Bronco matched O.J.’s DNA proﬁle

17. J ∗: Lab results supporting J

18. K: Blood on the driver’s side of the interior door handle of the Bronco matched O.J.’s DNA proﬁle

19. K∗: Lab results supporting K

20. L: Blood on the driver side carpet of the Bronco matched O.J.’s DNA proﬁle

21. L∗: Lab results supporting L

22. M: Blood on the steering wheel of the Bronco matched both O.J.’s and Nicole’s DNA proﬁles

23. M ∗: Lab results supporting M

24. N: Blood on the console of the Bronco matched both victims’ and O.J.’s DNA proﬁles

25. N ∗: Lab results supporting N

26. O: The blood trail on the ground leading to O.J.’s Rockingham residence matched O.J.’s DNA proﬁle

27. O∗: Lab results supporting O

81 28. P: Blood on the gate of O.J.’s Rockingham residence matched O.J.’s DNA proﬁle

29. P ∗: Lab results supporting P

30. Q: Blood on the ﬂoor of the master bathroom of O.J.’s Rockingham residence matched O.J.’s DNA proﬁle

31. Q∗: Lab results supporting Q

32. R: Blood in the foyer of O.J.’s Rockingham residence matched O.J.’s DNA proﬁle

33. R∗: Lab results supporting R

34. S: Blood found on the sock found in O.J.’s master bedroom matched both Nicole’s and O.J.’s DNA proﬁles

35. S∗: Lab results supporting S

36. T: Blood on the right hand glove found at O.J.’s Rockingham residence matched both victims’ and O.J.’s DNA proﬁles

37. T ∗: Lab results supporting T

38. U: Someone with O.J.’s blood type bled in O.J.’s Ford Bronco

39. V: Blood matching both victims’ blood types was found in O.J.’s Ford Bronco

40. W: Someone with O.J.’s blood type bled at O.J.’s Rockingham residence

41. X: Blood matching both victims’ blood types was found at O.J.’s Rockingham residence

82 Table 4.11: Prior probabilities for propositions relating to Blood stains evidence.

No. Prob. Values Prob. Values Prob. Values Prob. Values c 1 P(H5) 0.5 P(H|E A) 0.60 P(L|U) 0.85 P(P |W ) 0.98 c c c c c 2 P(H5) 0.5 P(H|E A ) 0.00 P(L|U ) 0.05 P(P |W ) 0.05 ∗ ∗ ∗ 3 P(A|H5) 0.90 P(H |H) 0.98 P(L |L) 0.95 P(P |P ) 0.98 c ∗ c ∗ c ∗ c 4 P(A|H5) 0.01 P(H |H ) 0.02 P(L |L ) 0.07 P(P |P ) 0.02 5 P(D|A) 0.75 P(I|H) 0.40 P(M|U) 0.85 P(Q|W ) 0.98 6 P(D|Ac) 0.00 P(I|Hc) 0.05 P(M|U c) 0.05 P(Q|W c) 0.05 7 P(D∗|D) 0.98 P(I∗|I) 0.99 P(M ∗|M) 0.98 P(Q∗|Q) 0.98 8 P(D∗|Dc) 0.02 P(I∗|Ic) 0.05 P(M ∗|M c) 0.02 P(Q∗|Qc) 0.02 9 P(E|A) 0.85 P(B|H5) 0.95 P(N|VU) 0.95 P(R|W ) 0.98 c c c c 10 P(E|A ) 0.00 P(B|H5) 0.01 P(N|VU ) 0.70 P(R|W ) 0.05 11 P(F |EG) 0.98 P(U|B) 0.98 P(N|V cU) 0.70 P(R∗|R) 0.98 12 P(F |EGc) 0.00 P(U|Bc) 0.07 P(N|V cU c) 0.05 P(R∗|Rc) 0.02 13 P(F |EcG) 0.00 P(V |B) 1.00 P(N ∗|N) 0.98 P(X|C) 1.00 14 P(F |EcGc) 0.00 P(V |Bc) 0.0015 P(N ∗|N c) 0.02 P(X|Cc) 0.0015 ∗ 15 P(F |F ) 0.95 P(J|U) 0.90 P(C|H5) 0.97 P(S|X) 0.85 ∗ c c c c 16 P(F |F ) 0.05 P(J|U ) 0.02 P(C|H5) 0.01 P(S|X ) 0.00 17 P(G|E) 0.20 P(J ∗|J) 0.98 P(W |C) 0.98 P(S∗|S) 0.98 18 P(G|Ec) 0.05 P(J ∗|J c) 0.02 P(W |Cc) 0.07 P(S∗|Sc) 0.02 19 P(G∗|G) 0.98 P(K|J) 0.75 P(O|W ) 0.98 P(T |X) 0.98 20 P(G∗|Gc) 0.02 P(K|J c) 0.20 P(O|W c) 0.05 P(T |Xc) 0.00 21 P(H|EA) 0.99 P(K∗|K) 0.98 P(O∗|O) 0.98 P(T ∗|T ) 0.98 22 P(H|EAc) 0.00 P(K∗|Kc) 0.02 P(O∗|Oc) 0.02 P(T ∗|T c) 0.02

83 Table 4.12: Posterior probabilities for propositions relating to Blood stains evidence.

Nodes Nodes Values O.J. committed the two murders H5 1.0000 O.J.’s blood was found at the murder scene A 1.0000 The blood of both victims and O.J.’s blood were found on his Ford Bronco B 0.9972 The blood of both victims and O.J.’s blood were found at O.J.’s Rockingham... C 1.0000 Blood stains found on the back gate of NBS house matched O.J.’s DNA profile D 0.9932 Bloody shoe prints found at the crime scene matched O.J.’ DNA profile E 0.9997 Bloody shoe prints at the crime scene came from Bruno Magli shoes F 0.9942 O.J. owns a pair of Bruno Magli shoes G 0.9955 Blood drops to the left of shoe prints found at crime scene matched O.J.’s DNA profile H 0.9999 O.J. had a cut on his left finger I 0.9296 Blood on the driver side of the exterior door handle of the Bronco matched O.J.’s DNA ... J 0.9994 Blood on the driver’s side of the interior door handle of the Bronco matched O.J.’s ... K 0.9932 Blood on the driver side carpet of the Bronco matched O.J.’s DNA profile L 0.9964 Blood on the steering wheel of the Bronco matched both O.J.’s and Nicole’s DNA profiles M 0.9964 Blood on the console of the Bronco matched both victims and O.J.’s DNA profiles N 0.9989 The blood trail on the ground leading to O.J.’s Rockingham residence matched O.J.’s DNA ... O 0.9996 Blood on the gate of O.J.’s Rockingham residence matched O.J.’s DNA profile P 0.9996 Blood on the floor of the master bathroom of O.J.’s Rockingham residence matched O.J.’s ... Q 0.9996 Blood in the foyer of O.J.’s Rockingham residence matched O.J.’s DNA profile R 0.9996 Blood found on the sock found in O.J.’s master bedroom matched both Nicole’s and O.J.’s DNA ... S 0.9964 Blood on the right hand glove found at O.J.’s Rockingham residence matched both victims’ and ... T 0.9996 Someone with O.J.’s blood type bled in O.J.’s Ford Bronco U 1.0000 Blood matching both victims’ blood types was found in O.J.’s Ford Bronco V 0.9972 Someone with O.J.’s blood type bled at O.J.’s Rockingham residence W 1.0000 Blood matching both victims’ blood types was found at O.J.’s Rockingham residence X 1.0000

84 Figure 4.6: Summary of DNA proﬁles in the Simpson case

85 Figure 4.7: A Bayesian Network for Blood stains

X T B

A W S

U V R D T* E D* Q H O N P J S* M K F G L R*

Q* N* H* J*

M* P* F* I G* K* L* O*

86 4.7 Sensitivity Analysis

In this section, we shall conduct a sensitivity analysis using two of our evidence categories, Motives and Opportunity to commit the murders. To do this, we can decide not to use any parts of the evidence in a particular network or change our probability assignments for any or combination of nodes in the network. With this change, we can then re-run the algorithm and obtain the resulting posterior probabilities, with which we calculate the c likelihood ratios based on our penultimate probanda H5 and H5. For the Motives network, we have testimony from Nicole’s ex-boyfriend, Keith and evidence from Nicole’s 911 tape of October 25th 1993. When we compiled the network, conditioning on all of these evidence, we obtained a likelihood ratio of 85.96 in favor of H5, i.e. in favor of O.J. committed the two murders. The Nicole’s 911 tape pertains to O.J.’s abuse of Nicole. We decided to exclude all the evidence relating to the abuse (i.e. evidence from the 911 call) and conditioned on only the evidence from the testimony of Nicole’s ex-boyfriend, Keith; in this case, the likelihood ratio reduces considerably to 4.68, but still in favor of H5. However, when we decided to condition on the evidence regarding the abuse only, those evidence extracted from Nicole’s 911 call, the likelihood ratio became very high again, to the tune of 80.30. Another variation we tried was to use all of the evidence but reversed all of our prior probability assignments on evidence nodes to reﬂect the fact that we do not believe (assign small probability values) any of the evidence. With that view, our likelihood ratio drops to .044 in favor of H5 (O.J. c committed the two murders) or 22.75 in favor of H5 (It was not O.J. who committed the two murders). There are many more possibilities and changes we can consider but we limit it to three for now for the sake of brevity, especially given the fact that these values are to be combined with similar values to be obtained from the second network regarding the Opportunity to commit the murders.

Another category of evidence in our analysis is the Opportunity to commit the murders. We used a lot of evidence for this category which led to a very extensive network. In total, we have 49 nodes with about 118 prior probability assignments. With our initial probability assignments and conditioning on all the evidence nodes, we obtained a likelihood ratio of

65.67 in favor of H5 which indicates that it is about 66 times as likely to obtain the evidence we have if we suppose O.J. was the killer in the death of his ex-wife and Ron Goldman than if

87 we suppose he was not. Two major witnesses for this category of evidence were Kato Kaelin who was living in the guest house of O.J.’s residence at the time of the murder, and the limo driver who drove O.J. to the Airport the night of the murder. When we excluded the evidence from these two witnesses and conditioned on the rest of the evidence, we obtained a likelihood ratio of 29.30 in favor of H5. Then we turned oﬀ all the rest of the evidence and conditioned only on evidence from Kato and the limo driver; from this we obtained a likelihood ratio of 5.17, also in favor of H5. Again, there are endless possibilities to be contemplated but we will limit it to these ones for now.

Finally, to calculate the aggregate likelihood ratio for the two evidence categories based c on H5 and H5, we would need to combine the likelihood ratios obtained from each category of evidence. Since we have a set of 4 likelihood ratio values from Motives category and another set of 3 likelihood ratio values from the Opportunity category, we will have a total of 12 aggregate likelihood ratios, each telling a diﬀerent story. We shall label the likelihood

∗ ∗ ∗ ∗ ratio values from the ﬁrst category of evidence as LE11 , LE12 , LE13 and LE14 . Similarly,

∗ ∗ ∗ values from the second evidence category will be labelled as LE21 , LE22 , and LE23 . Tables of likelihood ratios for Motives, likelihood ratios for Opportunity, and aggregate likelihood ratios are displayed below.

Table 4.13: Likelihood ratios for “Motives”.

No. Evidence type Likelihood ratio Values ∗ 1 All Evidence LE11 85.96 ∗ 2 Abuse evidence excluded LE12 4.68 ∗ 3 Abuse evidence only LE13 80.30 ∗ 4 Testimonies doubted (low credibility) LE14 0.044 (22.96)

For number 2 above, we excluded the abuse evidence by conditioning on all evidence nodes except B∗ and D∗. For number 3 above, we conditioned on the abuse evidence nodes only, B∗ and D∗.

∗ LE21 above was obtained by conditioning on all the evidence nodes (18 asterisked nodes)

∗ ∗ ∗ ∗ LE22 above was obtained by conditioning on all the evidence nodes EXCEPT O , N , P ,

88 Table 4.14: Likelihood ratios for “Opportunity to commit the murders”.

No. Evidence type Likelihood ratio Values ∗ 1 All Evidence LE21 65.67 ∗ 2 Kato and Limo driver testimonies excluded LE22 29.30 ∗ 3 Kato and Limo driver testimonies only LE23 5.17

∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ T , U , V , W , X , Z , A1, A4.

∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ LE23 above was obtained by conditioning ONLY on O , N , P , T , U , V , W , X , Z , ∗ ∗ A1, A4.

Table 4.15: Aggregate likelihood ratios for “Motives” and “Opportunity to commit the murders”.

No. Aggregate likelihood ratio Product Values ∗ ∗ 1 LE11 LE21 (85.96)*(65.67) 5645 ∗ ∗ 2 LE11 LE22 (85.96)*(29.30) 2519 ∗ ∗ 3 LE11 LE23 (85.96)*(5.17) 444 ∗ ∗ 4 LE12 LE21 (4.68)*(65.67) 307 ∗ ∗ 5 LE12 LE22 (4.68)*(29.30) 137 ∗ ∗ 6 LE12 LE23 (4.68)*(5.17) 24 ∗ ∗ 7 LE13 LE21 (80.30)*(65.67) 5273 ∗ ∗ 8 LE13 LE22 (80.30)*(29.30) 2353 ∗ ∗ 9 LE13 LE23 (80.30)*(5.17) 415 ∗ ∗ 10 LE14 LE21 (0.044)*(65.67) 2.89 ∗ ∗ 11 LE14 LE22 (0.044)*(29.30) 1.29 ∗ ∗ 12 LE14 LE23 (0.044)*(5.17) 0.2275 (4.40)

4.8 Combining the Stories

In our analysis, we constructed six Bayesian networks, one for each of the six evidence categories. Using Hugin’s software and its default (cluster) algorithm, we evaluated the probative value of each evidence category; some are small and others are substantial. As we explained earlier, the construction of each network was subjective, and the assigned priors were based on personal beliefs; others telling the same stories might tell them diﬀerently. They might present networks and numerical values that are completely diﬀerent from ours. In our analysis of the evidence, it is very possible that there were many evidence items that were inadvertently omitted and also possible that there were those we never knew and would

89 never know about. So, our collection of evidence used in our analysis is by no means complete, neither was the collection of evidence presented at the trial in this particular case and many other legal cases too. The truth of the matter is that it doesn’t matter how complete anyone thinks the evidence is, in any legal case, if one looks long enough and perseveres enough, there is always more evidence to be discovered. And, there are some evidence that are unknowable that would remain forever unknown. The whole concept of complete evidence is illusory in that it only resides in the figments of our imagination. No legal case was ever decided on complete evidence; what was frequently referred to as “complete” was actually relative and at best partial. But in spite of our partial collection of evidence in our analysis, we’ve been able to tell six different stories with six different categories of evidence. We feel the evidence considered in telling our stories is extensive enough to evaluate the combined probative value or strength of those stories. The six evidence categories that we analyzed - each with its own network - are: Motives, Knowledge of guilt, The Gloves, The weapon, Opportunity to commit the murders, and The ∗ ∗ ∗ ∗ ∗ Blood. The collection of evidence in each category is labelled as E1 , E2 , E3 , E4 , E5 , and ∗ E6 . The corresponding probative value for each network evaluated using likelihood ratio are

∗ ∗ ∗ ∗ ∗ ∗ denoted as LE1 , LE2 , LE3 , LE4 , LE5 , and LE6 . Each probative value represents an ending to the story we told with each network and we would employ Bayes’s rule to combine all of the six endings. The result of this combination is another likelihood ratio that grades the probative force of the evidence in all of the stories combined. If you recall, from chapter 2, ∗ 6 ∗ E = ∩j=1Ej and from equation (2.23):

LE∗ = L 6 ∗ ∩j=1Ej

∗ ∗ ∗ = LE1 ∩E2 ∩...∩E6

∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ = LE1 LE2 |E1 LE3 |E2 E1 ...LE6 |E5 ...E2 E1 (4.2)

Equation (4.2) implies that the six categories of evidence are not independent. However, if ∗ ∗ ∗ ∗ ∗ ∗ we now suppose that the six bodies of evidence in E1 , E2 , E3 , E4 , E5 , and E6 stories are inde-

c ∗ ∗ ∗ ∗ pendent, conditional on (H5 and H5), equation 4.2 then becomes LE =(LE1 )(LE2 ) ... (LE6 ), indicating that the combined probative value for the entire evidence is the product of the individual probative values for each body of evidence. In constructing our networks, we

90 exercised all diligence to make sure that the evidence items in all of our six evidence categories do not overlap, i.e., no particular evidence items is used in more than one category, in order to ensure that our evidence categories are mutually and completely independent. In spite of our diligence, we still can not claim such complete independence among all of our evidence categories because we might have inadvertently used an item in two or more evidence categories without realizing it. Moreover, we used many evidence items in our analysis to establish the presence of O.J. at Nicole’s house around the time of the murder, many of which did not come from the same evidence categories. For example, in Blood stains evidence category, we used the presence of O.J.’s blood at the crime scene and the presence of both victims’ blood in O.J.’s Ford Bronco to establish the presence of O.J. at Nicole’s house around the time of the murder. In the Opportunity to commit the murders evidence category, we also used the sighting of O.J. driving his Ford Bronco at an intersection close to the murder scene and along the route from the murder scene to his residence to also establish that O.J. was at Nicole’s house around the time of the murder. Using evidence items from diﬀerent evidence categories in this way may not necessarily ensure complete independence among the evidence categories. So, we submit that our overall aggregate likelihood ratio might have been overstated due to possible lack of complete independence among the evidence categories.

Table 4.16: Aggregate likelihood ratio for all the evidence combined.

No. Evidence Category Likelihood ratio Values ∗ 1 Motives LE1 85.96 ∗ 2 Opportunity to commit the murders LE5 65.67 ∗ 3 The Gloves LE3 89.90 ∗ 4 The Weapon LE4 122.5 ∗ 5 Knowledge of Guilt LE2 12.25 ∗ 6 The Blood LE6 131,120 7 Aggregate Likelihood ratio LE∗ 99,853,716,290,000

From Table 4.16 above, the aggregate likelihood ratio for all the evidence we considered is about 99,853,716,290,000. It is that many times as likely to obtain the evidence at hand if we suppose O.J. Simpson committed the two murders than if we suppose that he did not. As egregious as this number may appear to be, it is the probative value or strength of the totality

91 of the evidence we considered. And this is not surprising because most of our evidence items are those that favored the prosecution side - they were those evidence that the prosecution used to build the case against O.J. Simpson. With the size of the aggregate likelihood ratio that we obtained from the collection of evidence we analyzed, our analysis supports the prosecution’s contention that it was O.J.Simpson who committed those two murders on the night of June 12th, 1994 in Brentwood, California. Of course, there would be those evidence items that were used by the defense side to rebut or nullify the prosecution’s evidence - they were, however, small in number compared to the evidence presented by the prosecution and those evidence will be addressed in the next (conclusion) chapter.

92 CHAPTER 5

Conclusion

5.1 Conclusions and further work

In the Introduction chapter, we laid out the framework for this analysis and formulated our ultimate probandum or main hypothesis to the eﬀect that O.J. Simpson was guilty of the two murders. We set out to marshal the body of evidence generated in the case to prove this proposition - beyond reasonable doubt. From the state of California penal code (sections 187(a) and 189), we formulated our ultimate probandum and ﬁve penultimate probanda each of which needs to be proved to prove our ultimate probandum. However, we indicated that only one of them - that it was O.J. Simpson who committed the two murders - was (and still is) in dispute and that was the one we set out to prove using the evidence and a slew of interim probanda representing several stages of reasoning and sources of uncertainties. To prove this penultimate probandum, we partitioned the entire body of evidence into six sectors, each of which was analyzed using Bayesian networks. Our goal was to assess the probative strength of each of the six evidence sectors and combine them using Bayes’ rule. This was precisely what we did in Chapter 4.

We used two of the evidence categories namely, “Motives” and “Opportunity to commit the murders” to illustrate the concept of sensitivity analysis. For these two evidence categories, we made changes to our initial probability assignments and turned off and on some part of the evidence in order to conduct this sensitivity analysis. As a result, we were able to obtain different likelihood ratios for different scenarios. To compute the aggregate likelihood ratio for the two evidence categories combined, we multiplied the likelihood ratios from each evidence category. Given that we have 4 different scenarios for the Motives category and 3 different scenarios for the Opportunity category, we were able to obtain 12

93 different aggregate likelihood ratios, each telling a different story. These results are displayed in Table 4.15. In the first line of this table, we have an aggregate likelihood ratio value of 5,645 from the two evidence categories under our initial probability assignments. That means that, considering all the evidence items in these two sectors with our initial prior probability assignments, it is over fifty-six hundred times as likely to obtain the evidence at hand if we suppose O.J. Simpson committed the two murders than if we suppose he didn’t. The rest of the aggregate values in Table 4.15 can be interpreted in a similar fashion. But the last entry in Table 4.15 actually favors our alternative hypothesis, i.e., it is about four times as likely to obtain the evidence we have if we suppose O.J. did not commit the murders than if we suppose he did.

In Table 4.16, we present the likelihood ratio values obtained from our analysis for each of our six evidence categories. At the end of the table, we present the aggregate likelihood ratio of all the evidence categories combined which turns out to be about 99,853,716,290,000. This aggregate likelihood ratio represents our measure of the probative value or strength of all the evidence we analyzed. It doesn’t account for all the evidence we did not include, either inadvertently or by design, in our analysis. It is also the result of our subjective networks and assigned prior probability beliefs, and the assumption that our six networks are conditionally independent given H5.

In the case we analyzed, O. J. Simpson was the accused; he was tried in a court of law and was found not guilty of the crime - first degree murder - and was therefore acquitted and became a free man. He was subsequently tried in a civil court for the same crime but - unlike the criminal court - was found liable and ordered to pay a large sum of money to the victims’ families. One important reason for the different outcomes in the two trials is the fact that the standards of proof in the two cases are different. In the criminal trial, the standard of proof is “Beyond Reasonable Doubt” while that in the civil proceedings is “Preponderance of Evidence,” meaning more likely than not that the accused committed the crime - a less stringent requirement than beyond reasonable doubt. The purpose of our analysis is not to re-try Mr. Simpson as he has been tried and duly acquitted. Our intention is not to acquit or exonorate him; our objective, instead, is purely academic: to show the confluence of statistics and the law. Our result here may not even be tenable in the court

94 of law simply because some of our evidence might be considered hearsay or in violation of other legal rules or procedures and therefore not admissible in court.

As noted earlier, the probative force of the evidence we analyzed, that was determined via likelihood ratio, was egregiously high in favor of the prosecution. As also pointed out, this was because our evidence was mostly from the prosecution standpoint. The testimonies we used as evidence were from prosecution witnesses, and nothing from the defense side. But our analysis here strengthens the prosecution argument that it was O.J. Simpson who killed his ex-wife, Nicole Brown Simpson and her friend, Ron. L. Goldman on the evening of June 12th 1994 in Brentwood California. Of course, the defense for Mr. Simpson disputed this assertion by the prosecution by providing its own witnesses to rebut the testimonies from the prosecution witnesses. To present a balanced view, we would need to incorporate evidence from the defense side into our analysis. What we have done so far is the first phase of this type of research work; the second phase will be the incorporation of evidence from the defense side in which case our probability stories may perhaps take a different turn. However, to accomplish the second phase will require at least half as much time as we’ve expended completing the first phase. We would need to comb through the testimonies of about fifty-three witnesses who testified on behalf of the defense - each of whom testified for a period ranging from one to five days or more - searching for any part of their testimonies that would actually refute or contradict testimonies from the prosecution. The truth of the matter is that one doesn’t know if the testimonies of any witness are relevant and refute the defense until one goes through the entire transcript for that witness; given that some of the witnesses testified for as long as five consecutive days or more, that means we would need to go through the transcripts for each of those days and also perform this exercise for each of the fifty-three defense witnesses. But the enormous length of time required to do this is beyond the time-frame for writing a dissertation. This is an endeavor that should best be reserved for further work on this case.

So, our continuation of this research work will entail incorporating the evidence from the defense into our networks and analysis. Given that the defense’s job is to refute, contradict or weaken the prosecution stance and evidence, some of our likelihood ratio values in favor of the prosecution may be reduced considerably, thereby reducing the overall probative strength

95 of the evidence in favor of the prosecution. However, we do not anticipate that the present outcome of our analysis in favor of the prosecution will be reversed, especially because a cursory examination of some of the defense witnesses and evidence indicated that they did not refute or contradict the prosecution. This examination suggested that the defense strategy was not actually to refute or contradict the prosecution evidence; instead, it was to confuse the jury.

All of our networks constructed so far have less than twenty four nodes (a reasonable size for our current work) except two - “Opportunity to commit the murders” which has 49 and about 118 assigned prior probabilities, and “Blood stains” which has 41 nodes and about 88 assigned prior probabilities. It is possible that once we incorporate evidence from the defense into our networks, some of our smaller networks might also become very large. For the larger networks, we might be able to achieve better eﬃciency by subdividing them into smaller component parts which will result in what is termed as “Object Oriented Bayesian Networks” (OOBN), (see [10]). We will investigate this possibility in our future work.

96 APPENDIX A

BRIEF DESCRIPTIONS OF THE EVIDENCE ITEMS

As indicated in the Introduction Chapter, most of the evidence items used in our analysis were testimonies from many witnesses who testified during the Grand Jury proceedings, Preliminary hearings and Trial proceedings. So, the evidence used were obtained from the transcripts of all these various proceedings. In this section, we shall present brief descriptions of those evidence or testimonies used in our analysis. The transcripts of all the proceedings can be obtained through Westlaw database and many other sources. One particular source we found very useful was a site maintained by Jack Walraven where the records of many of the proceedings related to O.J. Simpson case are arranged in an organized and more user- friendly way. For access to the site, one should go to: www.simpson.walraven.org/. Many of the witnesses (not all) testified at more than one proceedings, especially for the prosecution. For example, many of the witnesses who testified at the Grand Jury proceedings also testified at the trial and/or preliminary hearing. In the brief descriptions of the evidence (testimonies) provided in this section, we also provide sources of the information in the form of citation. However, where the same witness testified in more than one proceedings, we only referenced one source since the witness provided essentially the same testimonies in all the different proceedings. In our electronic source of information, it turns out that the trial transcripts are not page-numbered while the transcripts from the other proceedings are. As a result, where a witness testified at the trial and any of the other proceedings, we cited the other proceedings that are page-numbered.

MOTIVES

97 Node B∗

At the trial, one of the items introduced into evidence was the transcript of the 911 call made by Nicole Simpson from her house on October 25th 1993 during an altercation between her and her ex-husband, O.J. Simpson. When the dispatcher asked her what her ex-husband looked like, she said it was O.J. Simpson and added, “I think you know his record.” When the dispatcher suggested that she should remain on the line, she said that she didn’t want to stay on the line and said of O.J., “He’s going to beat the (expletive) out of me.” Those statements combined suggested that there might have been some type of physical abuse going on in that relationship (see http : //walraven.org/simpson/911 − 1993.html).

Node C∗

One of the witnesses who testified for the prosecution during the Grand Jury proceedings was Mr. Keith Douglas Zlomsowitch, an ex-boyfriend of Nicole Brown Simpson, one of the victims. In his testimony, he stated that he met Nicole in the early part of 1992 and they remained acquainted until her death. He testified that he and Nicole were romantically involved for a brief period during that time after which they remained friends. He recounted a particular evening when he, Nicole and friends were at a restaurant he was managing, Mezzaluna. He testified that while they were at the restaurant, O.J. Simpson came in and leaned over their table, stared at him and all the other males at the table, introduced himself as O.J. Simpson and reminded them in a very “serious, if not scary” voice that Nicole was still his wife. That action in a way implied that O.J. wanted them to stay away from his wife (see http : //walraven.org/simpson/gj pt2.html, pages224 − 225).

Node D∗

As stated in B∗ above, the transcript of the 911 call made by Nicole Simpson from her house on October 25th 1993 during an altercation between her and her ex-husband, O.J. Simpson was introduced as evidence. As stated in the transcript, when Nicole made the call, she requested for police oﬃcers to be sent to her house and reported that her husband just broke into her house and was ranting and raving outside the front yard. The dispatcher could

98 hear O.J.’s voice in the background yelling and cursing and loud enough to be recorded on the tape while Nicole appeared to be scared, crying and at times sobbing. When the dispatcher asked her if such a situation has happened before, her reply was “many times.” This is a form of abuse (see http : //walraven.org/simpson/911 − 1993.html).

Node F ∗

In his testimony, Mr. Zlomsowitch recounted several intances of O.J.’s behavior which can arguably be construed as stalking. First, he spoke about the night when he, Nicole and friends were at one of the restaurants he was managing, Mezzaluna, when O.J. Simpson suddenly showed up, stared at them and reminded them in a very angry voice that Nicole was still his wife. Secondly, he spoke of another incident at another restaurant, Tryst, where O.J. suddenly showed up again, and stared at everybody at their table. Because of O.J.’s action, some of his friends felt uncomfortable and intimidated and decided to leave the restaurant. The third incident was when Mr. Zlomsowitch and Nicole went to a comedy club after which they went dancing at another club called Roxbury. After about 30 to 45 minutes in the club, Nicole went to him and told him that O.J. was in the club and they decided to leave. Finally, on another day when he and Nicole were at Nicole’s house, O.J. showed up and came through the back door unannounced, an action that startled both he and Nicole. All of these unexpected appearances of O.J. everywhere where Nicole and Mr. Zlomsowitch were reasonably constitute stalking (see http : //walraven.org/simpson/gj pt2.html, pages224 − 225, 230, 236 − 238).

∗ Node G1

Mr. Zlomsowitch in his testimony before the Grand Jury as mentioned in node C∗ said that when O.J. Simpson came to their table at the restaurant, leaned on the table, introduced himself and in a threatening voice said that Nicole was still his wife, he felt intimidated and was afraid of possible confrontation. He also indicated that when Nicole came back in the restaurant after going outside to speak with O.J., she was “visibly shaken.” Mr. Zlomsowitch also testiﬁed about a second incident of O.J.’s intimidation at another restaurant where he, Nicole, and other friends were guests. He testiﬁed that within a minute of the time they

99 were set at the table, O.J. walked into the restaurant and engaged in another episode of intimidation. Here is an excerpt from Mr. Zlomsowitch testimony:

When we were ﬁnally set, within a minute of the time we actually were set at the table, Mr. Simpson walked into the restaurant, walked directly by our table, looked at everybody at the table as he walked by, made it very clear that his presence was there, walked over to a table approximately 10 feet away from ours, pulled the chair sideways, as if to face our table directly, sat down and just stared at our table. This actually was so uncomfortable that one of the guests at our party felt so shaken she got up and left the restaurant. She said, “I just can’t handle this.”

Mr. Zlomsowitch indicated that O.J. was engaged in an episode of nonstop staring at them for a straight 8 to 10 minutes and more of his friends left the restaurant after they also became uncomfortable (see http : //walraven.org/simpson/gj pt2.html, pages229 − 230).

On the witness stand, Mr. Zlomsowitch recounted more incidents of O.J.’s intimidating behavior. He spoke of another incident when he and Nicole went to a comedy club in town after which they went dancing at another club, Roxbury. He said that after they’ve been in the club for about 30 to 45 minutes, Nicole came to her and said, “O.J. is here,” after which they decided to go back to Nicole’s house. After a brief stay at Nicole’s house, he left and went home. But the next day, Mr. Zlomsowitch went back to Nicole’s house and while he and Nicole were relaxing in the house, O.J. came into the house unannounced through the back door and startled both of them. (see http : //walraven.org/simpson/gj pt2.html, pages236 − 238)

∗ Node G2

In the 911 call of Nicole on October 25th 1993, it was apparent that there was cursing and yelling from O.J. directed at Nicole. She reported that he broke her back door down to get in the house; she was crying and sobbing, and felt scared enough to call 911 and requested for the presence of police at her house; All of these confrontations were coming

100 from a male ex-football player who is over six feet tall and heavily built directed towards a female of average built and just over 5 feet tall. That would be very intimidating (see http : //walraven.org/simpson/911 − 1993.html).

OPPORTUNITY TO COMMIT THE MURDERS

∗ Node A4

One of the Witnesses for the prosecution was Mr. Brian (Kato) Kaelin who was a guest living in one of the guest rooms at O.J.’s Rockingham residence around the time of the murder. Kato testiﬁed that on the night of the murder, he and O.J. went to McDonald to get something to eat and after they came back home, he parted with O.J. and went to his room after which he never saw O.J. again until around 11:00 p.m. when O.J. was getting ready to depart for the Airport (see http : //simpson.walraven.org/gj pt1.html, pages64−66, 78).

Node C∗

At the trial, the prosecution presented a phone record to show that on the night of the murder, Nicole spoke with her mother on the phone at about 9:40 p.m. This was to show that Nicole was still alive at that time and was subsequently killed sometime after 9:40 p.m. that night (see http : //simpson.walraven.org/jan24.html, see Ms. Clark).

Node E∗

Mr. Pablo Fenjves was another neighbor of Nicole who testiﬁed that on the night of the murder, while he was watching T.V., he heard a dog barking and wailing between 10:15 p.m. and 10:20 p.m. and that the barking and wailing went on for a long time (see http : //simpson.walraven.org/ph jul01.html, pages25 − 27).

Node F ∗

Mr. Steven Schwabb, one of Nicole’s neighbor, testiﬁed that on the night of the murder,

101 while he and his wife were walking their own dog ran into a large Akita dog wandering around with bloody paws. As they walked away, the large Akita dog followed them until they reached home barking and wailing in front of almost every house they passed by along the way (see http : //simpson.walraven.org/ph jul01.html, pages38 − 39, 41 − 43).

Node G∗

Mr. Sukru Botzepe was a neighbor of Nicole Simpson who testiﬁed for the prosecution. According to his testimony, he was living about 500 to 600 feet from the crime scene, and on the night of the murder, he came home around 11:40 p.m. and saw his neighbor, Steven and Linda Schwabb sitting with a big dog. From the conversation he had with the couple, he knew they had found the dog and he agreed to keep the dog with him till the next morning and give it to the animal shelter. After he took the dog to his apartment, the dog was very restless and nervous, going to the doors and windows, and running around the house. Given the restless and unusual behavior of the dog in the house, he and his wife decided to take the dog for a walk. Outside, they let the dog lead and the dog led them to the bodies of the two victims. According to him, the dog became more excited and was pulling him harder as they got closer and closer to the crime scene (see http : //walraven.org/simpson/gj pt2.html, pages171 − 173).

Nodes J ∗, K∗, and L∗

One of the witnesses for the prosecution was Ms. Jill Shively who was a resident of the same neighborhood as O.J. Simpson and his ex-wife, Nicole Simpson at the time of the murder. She testified that on the night of the murder, June 12th 1994,she was on her way to a food store to get something to eat, driving eastbound on San Vicente Blvd. At about 10:48 p.m. to 10:50 p.m., she came to the intersection of San Vicente and Bundy Drive where a white Ford Bronco with no lights on, heading northbound, ran through a red traffic light as she was entering the intersection with a green light on her side. According to her testimony, the Ford Bronco was forcibly stopped at the intersection when another car - a gray Nissan - traveling westbound on San Vicente blocked his path out of the intersection. She later identified the Driver of the Ford Bronco to be O.J. Simpson when the Driver

102 leaned out of the Bronco and started yelling at the Driver of the Nissan to move out of the way. As a result of the Ford Bronco running through the red light, Ms. Shively testified that she was forced to swerve towards a school and the Bronco also had to swerve away in order to avoid hitting each other. She testified that as O.J. Simpson was yelling at the Nissan car to get out of the way, the Driver of the Nissan looked very scared and tried to get out of the way but the two cars, Nissan and Bronco, kept moving back and forth (about three times) at the same time; this action infuriated O.J. more. Eventually, the Ford Bronco sped around the Nissan through the back and took off going north on Bundy (see http : //walraven.org/simpson/gj pt2.html, pages154 − 161).

Nodes N ∗ and O∗

Allan Park, the Limo driver, who took O.J. to the Airport the night of the murder testiﬁed that he went to O.J.’s house because he was instructed by his boss to go to 360 Rockingham Avenue to pick up O.J. Simpson and take him to the Airport to catch an 11:45 p.m. ﬂight to Chicago (see http : //simpson.walraven.org/gj pt2.html, page250).

Nodes T ∗, U ∗, W ∗, V ∗

∗ As a continuation of Kato’s testimony in node A4, he also testified that sfter he parted with O.J. between 9:40 p.m. and 9:45 p.m., while in his room, he called his then girlfriend, Rachel, and talked with her on the phone for a while. Kato testified that while he was on the phone, he heard a noise that sounded like a three-thump noise in the back of his room. He testified that the noise was so powerful that it shook the picture on the wall of his room. At that time, he thought that they just had an earthquake and asked Rachel if they just had an earthquake to which Rachel said “No.” He then grabbed a small flashlight and decided to go outside his room to check for the cause of the noise. Before hanging up the phone, he told Rachel that she should start to worry if she didn’t hear back from him in ten minutes. On his way to the back of his room, he then spotted a Limousine at the Ashford gate of the residence and walked over to open the gate and let the Limo driver in. After that, he helped put a golf bag that was placed by the front door area in the trunk of the Limo and asked the Limo driver if they just had an earthquake. The Limo driver told him “No” and that he was sitting in the

103 car and did not feel one (see http : //simpson.walraven.org/gj pt1.html, pages67 − 70, 74).

Node X∗

Mr. Kaelin also testiﬁed that after his brief conversation with the Limo driver, he attempted to check out the back of his room where the noise came from. He said that at the back of his room, there were two gates and after he got to the second one, he decided to come back out. When he came out, he saw O.J. talking with the Limo driver and he mentioned to O.J. about the noise he heard at the back of his room and asked him if there was an earthquake. He also asked O.J. for a better ﬂashlight to go and check the back of the room again (see http : //simpson.walraven.org/gj pt1.html, pages81 − 82).

∗ ∗ ∗ Nodes Z , A1 and P

Mr. Allan Park, the Limo driver, also testiﬁed that he arrived at O.J.’s residence at 10:25 p.m. and when he rang the bell of the residence at 10:40 p.m., there was no response. After a repeated ringing of the bell with no response, he called his boss at 10:50 p.m. and told his boss that he did not think that O.J. was home. He also noted that at the time of his arrival at the residence, there was only one light upstairs and no light downstairs which left most of the residence in the dark (see http : //simpson.walraven.org/gj pt2.html, pages250, 253, 255).

THE GLOVES

∗ ∗ Node A1 and A2

Officer Lance Riske of the Los Angeles police department was the first patrol officer to arrive at the Bundy crime scene. In his testimony at the trial, he testified that when he walked through the crime scene, he discovered a left-handed brown leather glove lying on the ground close to the feet of one of the victims, Ron Goldman. He also testified that when the Los Angeles police detectives Vannatter, Lange, Phillips and Fuhrman arrived, he walked them through the crime scene and showed them the glove he discovered. Each of the police detectives testified at the trial that when they arrived at the Bundy

104 crime scene, Oﬃcer Riske walked them through the crime scene and showed them the location of the glove he found (see http : //simpson.walraven.org/phjul05.html, page27 and http : //simpson.walraven.org/feb09.html, seeOfficerLanceRiske).

Node B∗

After leaving the Bundy crime scene, the four Los Angeles police detectives - Philip vannatter, Tom Lange, Ron Pillips, and Mark Fuhrman - went to O.J. Simpson’s Rockingham residence in order to inform him of the murder of his ex-wife and that his two young kids whom they found sleeping in the bedroom of his ex-wife were in custody of the police. At Rockingham residence, they did not find O.J. but met his daughter Arnelle and his house guest, Kato Kaelin. According to the testimony of one of the detectives, Mark Fuhrman, he spoke briefly with Mr. Kaelin, who informed him of an unusual noise and crashing he heard the night before from the back of his guest room that shook the picture on his wall. Consequently, he went behind the guest room to see if an intruder or a victim might have collapsed in the back of the room. According to detective Fuhrman’s testimony, on the narrow walkway behind the guest house that separates the O.J.’s residence and the adjacent property, he found a right-hand brown/black leather glove. He immediately called the attention of the other three detectives to his discovery and escorted each one of the detectives in turn to the location of the glove. Each of the detectives testified to the account of the discovery of the right-hand glove at O.J.’s residence as presented by detective Fuhrman (see http : //simpson.walraven.org/phjul05.html, pages31, 48, 53, 55 and http : //simpson.walraven.org/gjpt3.html, pages325 − 326, 330 − 331).

∗ Node C1

The Los Angeles police detectives Vannatter and Fuhrman on the witness stand at the trial testiﬁed that they believed that the right-hand glove discovered at the O.J. Simpson’s Rockingham residence, and the one discovered at the Bundy crime scene were a matching pair (http : //simpson.walraven.org/gjpt3.html, page333), (see http :

//simpson.walraven.org/phjul05.html, page54).

105 ∗ Node C2

One of the Prosecution’s witnesses was Ms. Brenda Vemich who was an employee of Bloomingdales department store in New York City in the 1990’s. According to her testimony, she was employed at the time as a store men’s gloves buyer. On the witness stand, she was shown people’s exhibits 77 and 164-A; exhibit 77 was the left-hand glove recovered from the Bundy crime scene while exhibit 164-A was the right-hand glove recovered from O.J. Simpson’s Rockingham residence. She identified the pair of gloves as Aris Isotoner gloves with four distinct characteristics: the vent palm, cashmere lining, brossier stitching, and extremely lightweight leather. She testified that these characteristics make this type of gloves unique and also testified that the pair of gloves shown to her were a matching pair based on her experience as a buyer of gloves (see http : //simpson.walraven.org/jun15.html, SeeBrendaV emich).

∗ Node C3

Another Prosecution witness was Mr. Richard Rubin. He was employed by Aris Isotoner, the glove manufacturing company who manufactured the gloves recovered from the crime scene and that recovered from O.J.’s residence. He was employed by the company as vice president and general manager in charge of design, manufacturing, production, raw materials, sales and marketing of all men’s gloves. He testiﬁed for the prosecution during the trial that, based on his experience in the above described capac- ity, the two recovered gloves, exhibits 77 and 164-A were indeed a matching pair (see http : //simpson.walraven.org/jun15.html, SeeRichardRubin).

Node D∗

∗ While Ms. Vemich, the Bloomingdales’ store associate that was introduced in node C2 , was on the witness stand at the trial, she was shown people’s exhibit 372-A and 372-B. Item 372-A was a copy of a receipt labelled “Bloomingdales receipt” and item 372-B was a microfiche copy of the same receipt. Using the microfiche exhibit, she identified this exhibit as a Bloomingdales credit card sales receipt and also identified some numbers on the receipt.

106 She testified that the number “517” on the receipt represents men’s accessories seasonal department, the number “222304” on the receipt represents employee’s I.D. number who was identified as Holina Phipps (the employee who made the sale and issued the receipt), the number “55” was the classification for gloves indicating that gloves were purchased, the number “953” identifies the vendor as Aris Isotoner, the number “70268” which (but for a mistake) should have been “70263” represents the style number indicating the style to be Aris light leather, the number “2” represents the quantity indicating that two pairs of gloves were purchased, and the numbers “77.00” and “30” represent the cost for the two pairs of gloves at thirty percent discount. Finally, she read the signed name on the receipt as Nicole Brown and testified that the descriptions given on the sales receipt fit the gloves ∗ that were earlier shown to her (which represents her testimony in node C2 above). So, the crux of her testimony here was that Nicole Brown purchased two pairs of Aris Isotoner light leather gloves at Bloomingdales department store in New York city on December 18, 1990 (the date on the receipt) for seventy-seven dollars at thirty percent discount (see http : //simpson.walraven.org/jun15.html, SeeBrendaV emich).

∗ ∗ Node E1 and E2

As explained in node D∗ above, Ms. Vemich testified that the receipt showed that Aris light leather gloves were purchased, the descriptions which fit those of the recovered pair of gloves. Mr. Rubin, the Aris Isotoner vice president and general manager who was also ∗ introduced in node C3 above, testified that the two recovered gloves were both Aris light leather gloves (see http : //simpson.walraven.org/jun15.html, SeeRichardRubin).

∗ ∗ Node F1 and F2

On the witness stand, Ms. Vemich testified that the light leather Aris Isotoner gloves were exclusive to Bloomingdales department store in the U.S.; that they were designed and developed for Bloomingdales, and were sold nowhere else either in the U.S., Europe or Asia. Mr. Rubin also testified to the fact that these particular type of gloves were exclusive to Bloomingdales as reflected in some excerpts from his testimony:

107 ...the model was exclusive to Bloomingdales. It was only manufactured and distributed to them. No other retailer in the United States had this model. And because of this particular type of sewing, which was unique to this model as well as the weight of the cashmere lining, the weight of the leather utilized and the way the vent is put into the palm, this could really not be any other style except 70263.

(http : //simpson.walraven.org/jun15.html, SeeBrendaV emich) Node H∗

∗ In node C2 , we explained that when Ms. Vemich was on the witness stand, she testiﬁed that the two gloves shown to her were a matching pair and also identiﬁed them as Aris Isotoner light leather gloves based on four charactersitics that were exclusive to those type of gloves. In node D∗, we also explained that Ms. Vemich concluded, based on the information on the Bloomingdales sales receipt that was shown to her that Nicole Brown Simpson purchased two pairs of Aris Isotoner light leather gloves from Bloomingdales store in New York city on December 18, 1990. Based on these two testimonies from Ms. Vemich, it can be inferred that the two recovered gloves were similar to the ones purchased by Nicole from Bloomingdales.

Node I∗

Mr. Collin Yamauchi was a Criminalist for the Los Angeles police department who testified for the prosecution at the trial and also during the grand jury proceedings. He was responsible for testing many of the blood stains recovered from the crime scene. He testified that the blood found on the right hand glove recovered from Rockingham residence of O.J. Simpson matched the DNA profile of O.J. himself and also those of the two victims, Nicole and Ron Goldman (see http : //simpson.walraven.org/gj pt3.html, page435).

THE WEAPON (Knife)

Node B∗

108 Dr. Irwin Golden who was employed as the Deputy Medical Examiner at the Los Angeles County Departmment of the Coroner, testﬁed for the prosecution before the Grand Jury and also at the trial. He was the Medical Examiner who conducted autopsies on the bodies of the two victims, Nicole and Ron Goldman. While on the witness stand, he was shown a stiletto knife similar to the one purchased by O.J. Simpson at the cutlery store. He testiﬁed that he believed that the type of knife shown to him was the same type used to kill the two victims (see http : //simpson.walraven.org/gj pt1.html, page 139).

Node D∗

Another witness who testified for the prosecution during the Grand Jury proceedings and also during the trial was Mr. Jose Camacho who was employed at Ross Cutlery store in Los Angeles as a Salesman around the time of the murder. He testified that about a month before the murder of Nicole and Ron Goldman, O.J. Simpson came to the cutlery store and checked out many of the different types of knives on display after which he showed interest in a particular one, decided to buy it but did not have enough money on him for the purchase. Mr. Camacho further testified that Mr. Simpson left the store without the purchase but returned about forty-five minutes later, at which time he purchased a stiletto type knife and paid for it in cash (see http : //walraven.org/simpson/gj pt2.html, pages193 − 195).

Node E∗

Mr. Camacho, the cutlery store salesman, also testified that after O.J. Simpson purchased the stiletto knife, he requested that the knife be sharpened. At that time Mr. Camacho gave the knife to his boss, Allen Wattenberg who sharpened the knife. Mr. Camacho testified that while the knife was being sharpened by Allen, he rang up the sale and O.J. paid for the knife with a hundred dollar bill. When he finished ringing up the sale, he went to the back of the store to get the knife from Allen and gave it to O.J. Simpson (see http : //walraven.org/simpson/gj pt2.html, pages202, 204).

Nodes F ∗ and G∗

109 Dr. Golden testified that in his examination of the two bodies during the autopsies, he observed that each of the two victims sustained several stab wounds to different parts of their bodies, some small and some large and deep. He described his account of the slash to the throat that extended from one ear to the other severing the jugular vein of each victim. Not only that, the police officers and the detectives who first responded to the crime scene also provided their accounts of the condition with which they discovered the victims which included multiple stab wounds, slashed throats and a large pool of blood

(see http : //simpson.walraven.org/gjpt1.html, page125). For complete autopsy report on Nicole and Ron Goldman, see (http : //simpson.walraven.org/autop − nb.html and http : //simpson.walraven.org/autop − rg.html).

Node H∗

Mr. Camacho, in his testimony to the Grand Jury and at the trial described the knife purchased by O.J. Simpson at the Ross Cutlery store as a stiletto knife with a single-edged blade (see http : //walraven.org/simpson/gj pt2.html, page196).

Node I∗

Dr. Golden also testiﬁed that the wounds on the bodies of both victims were consistent with those inﬂicted by a single-edged blade (see http : //simpson.walraven.org/gj pt1.html, page128).

Node J ∗

Dr. Golden, in his testimony, described in great details several stab wounds sustained by the two victims, the number, location and severity of those wounds. He concluded that, in his expert opinion, both victims died of multiple stab wounds sustained from the attacks on that night of June 12th 1994 (see http : //simpson.walraven.org/gj pt1.html, page133).

KNOWLEDGE OF GUILT

Node D∗

110 On Friday June 17th 1994, the Los Angeles police department decided to arrest and charge O.J. Simpson for the murder of his ex-wife, Nicole Brown Simpson, and her friend, Ron Goldman. For the booking process, the Police department requested through Robert Shapiro, one of O.J.’s Lawyers, that O.J. should turn himself in. After Robert Shapiro informed O.J. of the Police request, he showed no objection; however, instead of complying with the police order, O.J. - without any consultation with his Attorney - took to the freeway and led the police on the infamous white Ford Bronco chase that lasted for about two to three hours. During this time, O.J. with his friend Al Cowlings in the vehicle with him, drove around on a Los Angeles freeway threatening to take his own life. It was a sight to behold as many people glued their eyes to their television sets watching the drama unfolding before their eyes. With several Police cars at his tail, O.J. decided to end the chase and headed back home where he surrendered to the Police (see [11], pages 185, 188-196).

Node G∗

During the trial, the Police testimony was that after O.J. surrendered himself to the Police they seized and searched the white Ford Bronco that was used in the chase inside which they found O.J.’s passport, a disguise and ten thousand dollars in cash.

Node H∗

During the white Ford Bronco chase where O.J. Simpson rode around for several hours on Los Angeles freeway, he was actually a passenger in the vehicle while his friend, Al Cowlings was at the wheel. At one point during the chase, Al Cowlings called the police on his cell phone informing them that O.J. had a gun to his head and was threatening to shoot and asked the police to back oﬀ on the chase in order to avoid the fatal consequence of O.J. killing himself (see [11], pages 190, 195 ).

THE BLOOD STAINS

Almost all the evidence nodes in this network are lab results of blood stains taken from the

111 crime scene, O.J.’s Rockingham residence and his Ford Bronco. DNA testing was performed on these blood stains, and as indicated in section 4.6, the DNA testing was performed by three separate agencies the Los Angeles Police Department (LAPD), the California Department of Justice DNA Laboratory (DOJ) and Cellmark Diagnostics (CMD), a private company located in Gaithersburg, Maryland. The results of the lab tests indicate that the blood stains matched the DNA proﬁles of both victims and O.J. Simpson. These lab results were used to support many of our propositions in the blood stains network. The descriptions of the stains and their locations are presented in section 4.6 and the summary of the results can be found in Figure 4.6. There is no point in duplicating the information regarding the evidence here.

112 REFERENCES

[1] Murphy Kevin. A Brief Introduction to Graphical Models and Bayesian Networks. A Tutorial on Bayesian Networks, 1998. (document), 3.2.1, 3.3

[2] Schum D.A. The Evidential Foundations of Probabilistic Reasoning. Evanston, IL, Northwestern University Press:213–220, 1994. 1

[3] I. Good. Good thinking: The Foundations of Probability and Its Applications. University of Minnesota Press, Minneapolis., 1983. 2.4

[4] Kadane J.B. and Schum D.A. A Probabilistic Analysis of the Sacco and Vanzetti Evidence. John Wiley and Sons, Inc., 1996. 2.5, 2.5

[5] Heckerman David. A Tutorial on Learning With Bayesian Networks. Technical Report : Microsoft Research, 1996. 3.1.1 [6] Lauritzen S.L. and Spiegelhalter D.J. Local computations with probabilities on grahical structures and their application to expert systems. Journal of Royal Statistics Society B, 50(2):157–194, 1988. 3.1.2

[7] Anderson T., Schum D.A., and Twining W. Analysis of Evidence (Second Edition). Cambridge University Press, 2005. 4.1

[8] Thompson W. C. DNA Evidence in the O.J. Simpson Trial. University of Colorado Law Review, 67:827–857, 1996. 4.6

[9] Weir B. S. DNA statistics in the Simpson matter. Nature Genetics, 11:365–368, 1995. 4.6

[10] Hepler A. and Philip D. Object-Oriented graphical representations of complex patterns of evidence. Law, Probability, and Risk, 6:275–293, 2007. 5.1

[11] Simpson O.J. and Goldman R. If/I DID IT, confessions of THE KILLER. Beaufort Books, New York., 2007. A

113 BIOGRAPHICAL SKETCH

Kunle M. Olumide

Kunle M. Olumide is a native of Windsor, Connecticut with family roots in Nigeria, a West African country. Prior to coming to Florida State University, He received his Bachelor’s degree in Mathematics from The City College of New York and a Master’s degree in Statistics from The University of Connecticut. He also received a J.D. degree in Law also from The University of Connecticut School of Law. At Florida State, he received another Master’s degree in Biostatistics and just completed his Ph.D in Statistics this Fall, 2010. His research interests are in Biostatistics and Application of Statistics in Law.

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