Proc. Natl. Acad. Sci. USA Vol. 92, pp. 11741-11745, December 1995 Medical Sciences

Inferring identity from DNA profile evidence (forensic science/statistical inference) DAVID J. BALDING* AND PETER DONNELLYt *School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London, El 4NS, United Kingdom; and tDepartments of Statistics, and Ecology and Evolution, University of Chicago, 5734 University Avenue, Chicago, IL 60637 Communicated by Newton E. Morton, University of Southampton Princess Anne Hospital, Southampton, United Kingdom, July 24, 1995

ABSTRACT The controversy over the interpretation of surprising is the evidence if the defendant is not the culprit, and DNA profile evidence in forensic identification can be attrib- hence the more the jury ought to be inclined to believe that uted in part to confusion over the mode(s) of statistical culprit and defendant are the same person. It is difficult, inference appropriate to this setting. Although there has been however, to make this intuition precise. substantial discussion in the literature of, for example, the The lack of theoretical underpinning of the profile fre- role of population genetics issues, few authors have made quency as a measure of evidential weight is the source of much explicit the inferential framework which underpins their confusion that surrounds questions such as the following. arguments. This lack of clarity has led both to unnecessary (i) Of what relevance is the fact that profile frequencies debates over ill-posed or inappropriate questions and to the vary among human populations? In which population neglect of some issues which can have important conse- should the profile frequency be estimated? quences. We argue that the mode of statistical inference which (ii) How is the DNA evidence, summarized by the profile seems to underlie the arguments of some authors, based on a frequency, to be incorporated with the other evidence? hypothesis testing framework, is not appropriate for forensic (iii) How should inference be affected if one or more of the identification. We propose instead a logically coherent frame- defendant's close relatives are not excluded by the other work in which, for example, the roles both of the population evidence from being among the possible culprits? genetics issues and of the nonscientific evidence in a case are (iv) How should inference be affected if it is known that the incorporated. Our analysis highlights several widely held defendant is one of a group of possible culprits whose misconceptions in the DNA profiling debate. For example, the DNA profiles were investigated? profile frequency is not directly relevant to forensic inference. (v) What can be inferred if the "match" between the Further, very small match probabilities may in some settings defendant's profile and the culprit's profile is equivo- be consistent with acquittal. Although DNA evidence is typically cal-for example, because of some missing bands from very strong, our analysis of the coherent approach highlights a degraded sample? situations which can arise in practice where alternative methods Without a sound theoretical basis for inference, the resolution for assessing DNA evidence may be misleading. of these questions is extremely difficult and, in fact, the current extensive debate has not resolved them. Although it may be difficult to answer such questions exactly in particular cases, it is 1. Introduction: Inference in Forensic Identification nevertheless important to have a theoretical framework in which they can be answered in principle. In this paper we present such In criminal cases involving DNA profiles, the jury may be a framework. It has been accepted by both prosecution and presented with evidence that (i) the culprit has a certain defence in some U.K. cases, including appeal cases. genetic type, (ii) the defendant has the same genetic type (to In Section 2, we discuss inferential frameworks based on within measurement error), and (iii) the shared genetic type is classical hypothesis testing and argue that these are unsatis- rare. The jury has the task of using this evidence, together with factory in the criminal trial setting. Next, in Section 3, we any other evidence presented to it, to decide whether or not the describe a coherent framework for forensic inference, in which defendant is the culprit. The jury's task can formally be viewed it is conditional match probabilities, and not profile frequen- as a statistical inference problem: it is required to accept or cies, which are directly relevant to inference. The effects of reject a hypothesis (that the defendant is the culprit) on the both relatedness and population genetics issues enter the basis of data (evidence), part of which is statistical in nature discussion through conditioning on the defendant's profile, as (that measuring the rarity of the genetic type). discussed in Section 4. Further consequences of the coherent Most current practice involves an expert witness reporting to approach, which can be important in practical casework, are the jury an estimate of the profile frequency, which is the discussed in Section 5. relative frequency in some population of the DNA profiles Collins and Morton (1) have previously discussed methods which, due to measurement error, cannot be distinguished of statistical inference appropriate to forensic identification from the culprit's DNA profile. The profile frequency is often using DNA profiles. In common with the analysis presented interpreted in terms of the probability that a randomly selected here, those authors advocate a central role for likelihood ratios individual would have the profile. and, consequently, conditional match probabilities rather than Surprisingly, reasons for using the profile frequency to profile frequencies. The two approaches differ in their meth- quantify the DNA evidence are rarely discussed. Moreover, ods for combining the different likelihood ratios correspond- there appears to have been little consideration of the crucial ing to the various levels of relatedness between defendant and question of the logical connection between it and the proba- possible culprit. Collins and Morton propose a sequence of bility which is of direct interest to the jury-namely, the hypothesis tests, whereas the present approach employs a probability that the defendant is the culprit. It seems intuitively weighted sum of the likelihood ratios, with the weights being reasonable that the smaller the profile frequency, the more the probabilities, based on the non-DNA evidence, of each possible level of relatedness. The publication costs of this article were defrayed in part by page charge The DNA evidence at trial relates directly to the identity of payment. This article must therefore be hereby marked "advertisement" in the source of crime samples. To simplify terminology, we accordance with 18 U.S.C. §1734 solely to indicate this fact. equate "is guilty" with "is the source of the crime sample." 11741 Downloaded by guest on September 26, 2021 11742 Medical Sciences: Balding and Donnelly Proc. Natl. Acad. Sci. USA 92 (1995) 2. Hypothesis Testing ical to established principles of criminal justice. Although such long-run success rates may be of some interest, interpreting One possible rationale for the use of the profile frequency to them in the context of a specific case is, at best, problematic. quantify the identification evidence, a rationale which seems to be assumed implicitly by many authors, is in terms of the 3. A Coherent Framework for Inference significance level associated with a particular hypothesis test. Suppose that the jury considers only the following two hy- In criminal trials, the important issue is how an assessment as potheses. to the guilt or innocence of the defendant should be made in R: The defendant has been chosen at random from a the light of all the evidence presented to the jury. There exists population of innocent individuals; a substantial literature on methods for assessing and revising G: The defendant is the culprit. beliefs in the presence of uncertainty. Loosely speaking, a The legal maxim "innocent until proven guilty" would con- collection of beliefs is said to be coherent if it avoids internal strain the jury not to accept hypothesis G unless it is persuaded logical inconsistencies. Coherent, quantitative belief systems by evidence to do so. Hypothesis R would thus play the role of must behave as if they are governed by the usual laws of the null hypothesis, in statistical terminology. probability (for example, see ref. 3 and references therein). After observing the culprit's profile, a critical region can be When additional evidence becomes available, beliefs (quanti- identified that consists of profiles which, because of measure- fied as probabilities) must be updated according to Bayes ment error, cannot be distinguished from it. If the defendant's theorem. Because of this prominent role of Bayes theorem, the profile falls in the critical region, then the null hypothesis, R, coherent approach is sometimes labelled "Bayesian." is rejected and its rival, G, is accepted. The conventional Arguments for the use of probabilities in assessing evidence measure of "confidence" associated with this decision is the presented at trials are not new. See, for example, the collection significance level of the test-that is, the probability of ac- of papers in ref. 4 and, for discussions of the coherent approach cepting G if R is true, which in this context is the profile to scientific identification evidence, refs. 5 and 6. Although frequency in the population specified by R. these arguments have not always been accepted in general An immediate criticism of this hypothesis testing rationale settings, in the particular case of DNA evidence, presented in for use of the profile frequency is the lack of justification for court in numerical terms, the problem of its combination with considering the "random selection" hypothesis, R, as the rival other evidence cannot be avoided. The arguments for the to the hypothesis of guilt, G. The mechanism of random coherent approach in this context are compelling. selection does not provide a reasonable model for the process Note that we regard the general discussion of the assessment by which innocent defendants are actually obtained. Because of evidence and the particular method described below in of the arbitrary nature ofR, the problem of specifying in which connection with DNA profiling evidence to be normative population the profile frequency should be measured cannot rather than descriptive. That is, it relates to an "in principle" be resolved. solution of the problem rather than a description of the way in In criminal trials, the jurors must base their verdict on all of which jurors actually arrive at verdicts. Knowledge of the the evidence presented in court. Hypothesis testing approaches "correct" method for assessing DNA evidence is valuable in accept or reject the hypothesis of innocence solely on the basis highlighting errors and misunderstandings which may follow of the DNA evidence. A fundamental weakness of such from other approaches (7, 8) and in assessing possible approx- methods is that there are no reasonable principles for incor- imations or simplifications. In particular, the framework pre- porating the non-DNA evidence into the decision process. It sented here allows the resolution, in principle, of all the might be argued that the significance level of the hypothesis questions listed in Section 1. test (based on the DNA evidence) could be varied according Within the coherent framework, the problem of incorpo- to the strength of the other evidence. There seems to be no rating the DNA evidence thus becomes one of using it to basis for quantifying this suggestion and its implementation update the probability, based on the other evidence, that the could not be other than ad hoc. defendant is the culprit. It is convenient to frame the discus- Another drawback of hypothesis testing approaches is that sion in terms of O(G), the odds against the hypothesis of guilt the outcome of such a test can depend crucially on the method (after taking the identification evidence into account). These by which the defendant was identified. For example, suppose odds can be converted into the probability of guilt P(G) by the that suspects are tested sequentially until one is found to match formula the culprit's profile. In principle, a sufficiently thorough search is guaranteed to result in a matching profile, and thus the 1 significance level associated with the evidence would be 1. In P(G) = 1 + O(G) [1] other words, for an ideal search the hypothesis testing ap- proach assigns no weight to the DNA evidence. In practice, it Under certain plausible assumptions (9), O(G) can be ob- may not be possible to examine every possible culprit, so that tained as a weighted sum of conditional probabilities of profile the search could have terminated without a match. Although possession. More precisely, writing s and C for the name of, the significance level associated with the search would then be respectively, the defendant and the culprit, < 1, it may often be substantial and will in any case be difficult to assess. = = Similar difficulties arise in the large number of realistic cases O(G) PP(Cij9s)P(CP(C = S)'i) [2] in which a hypothesis such as R is inappropriate-for example, 3(iVis when a database of DNA profiles has been searched and precisely one profile in the database has been found to match where we introduce I;S for the (measured) DNA profile of the (2). Information about the method used to identify the defen- defendant and ti (i 0 s) for the event that the profile of dant is sometimes not admissible as evidence, in which case it individual i matches the defendant's profile. Although not would seem impossible to employ a hypothesis-testing infer- explicit in the notation, each probability in Eq. 2 is conditional ential approach. on all the other evidence. For example, P(C = s) denotes the More generally, measures of "precision" in the hypothesis probability that the defendant is the culprit based on all the testing paradigm, in terms of the proportion of incorrect evidence other than the defendant's DNA profile. rejections of the null hypothesis in an indefinite sequence of The summation in Eq. 2 is over every individual, other than independent repetitions of the same procedure, seem antithet- s, not excluded by the other evidence from being a possible Downloaded by guest on September 26, 2021 Medical Sciences: Balding and Donnelly Proc. Natl. Acad. Sci. USA 92 (1995) 11743 culprit. Alternatively, one could think of the summation as session induced by shared ancestry will imply that P(ZJI9S) > being over every person on earth, for many of whom the P(6i) for individuals i with an ethnic background similar to that corresponding value of P(C = i)/P(C = s) will be negligible or of the defendant. The strengths of these correlations depend zero. In practice it is not necessary to contemplate explicitly on the genealogy of the population and the details of the every possible culprit. Instead, evaluation can proceed by mutation mechanism at the loci involved. In simple population grouping together individuals who have a similar level of genetic models, the effect of this correlation depends on a relatedness to the defendant s and who consequently have a single parameter, often called FST. In such models, formulas similar value for P(%iJ5;;). For each such group, one then need for match probabilities are available, in terms of the allele only assess the probability, based on the non-DNA evidence, frequencies and FST (14, 15). However, care is needed in that the culprit is a member of the group, rather than consider applying these formulas because the assumptions of the un- separately each member of the group. Broadly speaking, this derlying models may not be appropriate for forensic loci. will typically require consideration of close relatives of the Further, only limited data for assessing FST values are yet defendant, persons not directly related to the defendant but available on the relevant demographic scales. Published esti- sharing ancestry on an evolutionary time scale, and other mates ofFST at forensic loci are usually small (16, 17), typically persons unrelated to the defendant. Some examples of the much smaller than the values for traditional loci (18), although evaluation of P(G) under simplifying assumptions are given in recent analyses of forensic data using a different method of ref. 10. estimation (D.J.B. and R. A. Nichols, unpublished work) sug- An important feature of Eq. 2 is that there is a distinct term gest appreciable values of FST which cannot reasonably be for each possible culprit. One need not consider any hypo- ignored in forensic settings. thetical "random" individual, a concept that has led to con- a siderable confusion. There has been considerable debate over Aside from empirical issues, match probability is quite the choice of the appropriate "reference population" (11), the distinct, as a matter of logic, from a profile frequency. This conceptual population from which, in the hypothesis testing distinction has a number of important consequences for fo- framework, an innocent suspect has been chosen randomly. rensic inference. For example, it has been argued (19, 20) that The analysis described above shows that this question is not genotype frequency estimates based on the product rule are relevant. "conservative" because they overestimate the population gen- Eq. 2 involves conditioning on the DNA profile of the otype frequency in simple models of population substructure. defendant. There is an equivalent equation which conditions These arguments are misdirected, in focusing on profile fre- instead on the profile of the criminal. quencies rather than (conditional) match probabilities, and are misleading, since the effect of substructure in these models is 4. Match Probabilities to increase, relative to the panmictic case, all relevant match probabilities for individuals in the same subpopulation as the The analysis of the previous section establishes that the defendant (14). strength of the DNA evidence does not depend on profile frequencies but on the conditional probabilities P(6iJi;). This 5. Practical Consequences of Coherence observation, first emphasized by Morton (12), follows from the principle that weight of evidence should be assessed via 5.1. Approximations. To simplify the presentation of DNA likelihood ratios and does not rely on the coherent approach evidence, it may be desirable to introduce approximations into for its justification. We will refer to the conditional probabil- Eq. 2 which require only one or two match probabilities. Eq. ities P(%iJ9;;) as matchprobabilities. Others have used this term 2 may be rewritten as to refer to profile frequencies, which may be misleading because a match involves two profiles that are the same or = similar, whereas a profile frequency involves only one profile. 0(G) P(C s) aye, [3] The probabilities P(%iJ9;) will in general vary with i, de- pending on the degree of relationship (in the everyday sense in which and in the sense of sharing ancestors on an evolutionary time between individual i and the defendant s. In most = scale) = i) forensic cases, there is thus more than one relevant match Pave PP(WiI;;)P(C probability (equivalently, more than one likelihood ratio). ios Approximations which involve a small number of match prob- denotes the appropriate "average" match probability. Unfor- abilities will be discussed in Section 5.1. tunately, evaluation OfPave depends on the jury's assessment of While population databases may be helpful in assessing the other evidence. It cannot be undertaken by the forensic profile frequencies, they do not allow direct assessment of scientist. While Eq. 3 may help to clarify the intuition behind match probabilities. These require, in addition to suitable data, 1 not in sense a modeling of the relevant correlations on the basis of statistical Eqs. and 2, it is useful the of providing single and population genetics theory. In general there will be match probability which the forensic scientist can report to correlations that arise because of our uncertainty over profile court. frequencies, which may be due to a number of factors (9). We Ignoring for the moment close relatives of the defendant, a concentrate here on genetic correlations. conservative choice for a single match probability would be to The role of population genetics issues in forensic DNA report the largest value of P(ZJI9i) over possible alternative analysis has been widely discussed. Much of the debate has culprits i. This will typically be the match probability for focussed on the appropriateness or otherwise of the "product individuals i in the same subpopulation as the defendant. In a rule" (13) for estimating profile frequencies. The coherent case in which this applies, and for which other evidence analysis of Section 3 shows this debate to be misconceived, since excludes close relatives, an upper bound for Eq. 2 is the appropriate focus is not a profile frequency but the condi- tional probabilities P(%iJ9;;) for different possible culprits i. 1 - P(Glnon-DNA evidence) The effect of any population stratification is exactly incor- P(Glnon-DNA evidence) porated in the coherent analysis by the conditioning on the defendant's profile and the (weighted) averaging over possible P(esub Is) alternative culprits. The positive correlations in profile pos- P(Glnon-DNA evidence)' Downloaded by guest on September 26, 2021 11744 Medical Sciences: Balding and Donnelly Proc. Natl. Acad. Sci. USA 92 (1995) where P(fsubjIY) is the conditional probability that a particular prosecution) the only incriminatory evidence was the DNA (unrelated) individual from the defendant's subpopulation will profile match between defendant and criminal. In contrast, the match. Use of Eq. 5 as a conservative bound for Eq. 2 has victim, who maintained that she had a good view, and memory, obvious practical advantages (when close relatives are exclud- of her attacker's face, testified without challenge that the ed). defendant did not resemble the man who attacked her. In Further, whatever its exact value, the match probability for addition an apparently credible witness gave the defendant an unrelated individuals in the defendant's subpopulation is likely alibi at the time of the offense. Our point is that there will be to be small for a four-or-more-locus profile, so that if the effect (a minority of) cases in which extremely small values (say 10-5 of the non-DNA evidence is to cast reasonable suspicion on the or smaller) for P(C = s) are plausible. defendant, then the (overall) case against him/her will be very A further consequence of such scenarios is that the exact strong. Note, however, that this conclusion depends on an value of the match probability can be important, in contrast to assessment of the other evidence in a case, which is not in the the widespread view that debates over errors of 1 or 2 orders domain of an expert witness. Further, it does not obviate the of magnitude are "purely academic" (21) when the match need for care and accuracy in the statistical evaluation and probability is very small. In examples like those outlined in the presentation of DNA evidence. previous paragraph, if by ignoring sources of uncertainty a 5.2. Close Relatives. The report of the U.S. National Re- forensic scientist reported a match probability of 10-8 when a search Council (ref. 13, p. 87) advocated that "whenever there more careful analysis might lead to 10-6 as an appropriate is a possibility that a suspect is not the perpetrator but is related value, the outcome of the trial could be affected. Since it is not to the perpetrator, this issue should be pointed out to the the role of a forensic scientist to assess the nonscientific court." In fact, the substantially higher match probabilities for evidence, it is not in general possible for her/him to know relatives can have an important effect even in cases in which whether or not this may occur in a particular case. there is no direct evidence suggesting that the perpetrator may 5.4. The Effect of Searches. As discussed in Section 2, be a relative of the defendant. hypothesis testing approaches have particular difficulty in Other than identical twins, the most important effects dealing with the method by which the defendant was identified, involve siblings of the defendant whose DNA profiles are not which may have involved a search of possible culprits or a available. A direct consequence of Eq. 2 is that the relevant "trawl" through a DNA profile database. These situations are issue is not whether or not there is reason to suspect the readily accommodated in the coherent framework. In a wide defendant's siblings, but the strength of the evidence against range of settings, the DNA evidence is slightly stronger when them relative to the strength of the non-DNA evidence against it is obtained after a search, compared with the case of only one the defendant. It may in some cases be plausible that the suspect, and hence it slightly favors the defendant to ignore the non-DNA evidence has approximately the same weight for the search (9, 23). Although this result conflicts with conclusions defendant as for some or all of the siblings. In this case it drawn in a hypothesis testing framework (1), the intuition is follows from Eqs. 1 and 2 that P(G), the probability of the that the search excludes other individuals from being possible defendant's guilt, is at most 1/(1 + nmx), in whichx denotes the culprits. That the hypothesis testing approach is misleading can number of such siblings and m denotes the sibling match be illustrated by considering the situation in which everyone on probability. For four-locus DNA profiles, m is typically about earth has been profiled and only one found to match. From the 1%. Thus there may be reasonable doubt about the defendant's hypothesis testing perspective, this evidence is of no value since guilt due to the defendant's siblings alone, even in cases in the search was guaranteed to find a match. The coherent which there is no specific reason to suspect them. A practical approach gives the correct answer: the evidence amounts to consequence is that satisfactory prosecutions will require proof of guilt (assuming here no false exclusions). additional evidence tending either to inculpate the defendant Although the DNA evidence may be slightly stronger in the or to exculpate the siblings. One possible source of such further case of a search, the overall case against the defendant may evidence is to profile the siblings, if this is feasible, although often be weaker because there may be little or no other non-DNA evidence may also suffice. evidence and consequently a large pool of possible culprits. 5.3. Limited, or Exculpatory, Non-DNA Evidence. The per- (For a thorough discussion, see ref. 2.) ceived strength of DNA evidence has led to cases in which 5.5. Incorporating Laboratory Errors. Our discussion of there is little or no evidence against the defendant other than Eq. 2 involved some simplification. In place of P(WiJ5s) in that the DNA evidence. Even if close relatives are unequivocally equation, one should use P(WcJIs, C = i). If Wi and is were excluded, there may be many unrelated individuals who, if not interpreted in terms of actual (multilocus) genotypes, then for the DNA evidence, would be in much the same situation P(fcl9s, C = i) would usually be the same as PffiJ5;). That is, as the defendant. In other words, there may be many i such that conditional on the defendant's genotype (but not on the P(C = i)/P(C = s) is close to unity. criminal's genotype) knowledge that a particular individual is Similar issues arise when there is substantial exculpatory the criminal will not change his/her probabilities of genotype evidence, such as a convincing alibi, which conflicts with possession. (See ref. 9 for a fuller discussion.) inculpatory DNA evidence. Such cases can arise when an In fact, Wc and i* are defined not in terms of actual individual not directly under suspicion is noticed, for reasons genotypes but in terms of the profiles measured and reported either unrelated to the crime or which are inadmissible as by the forensic laboratory. If an error occurs, the criminal and evidence, to have a matching DNA profile. defendant profiles could be reported to match even though the In such cases, even very small match probabilities do not individuals have nonmatching genotypes. This possibility is necessarily allow a satisfactory prosecution: although each incorporated in the analysis exactly by using P(fcJI9, C = i) in P(ffjjJ) contributing to Eq. 2 is small, the sum of many such place of P(fil5-) in Eq. 2. The probability P(WScI5;, C = i) is terms may be nontrivial. In some cases it might be appropriate thus the sum of the probability that individuals i and s have to consider, for example, the number of males aged between, matching genotypes and no false exclusion error occurs and the say, 16 and 50 who could have been at the scene of the crime. probability that the genotypes do not match and a false (Note that we are not advocating the general use of prior inclusion error occurs. This latter probability could be sub- probabilities given by the reciprocal of census figures.) In large stantially larger than the former (7, 22), in which case ignoring cities, this number could be of the order of 106, in which case the possibility of such errors would be seriously prejudicial to even a match probability as small as 10-7 may not be convinc- the defendant. Note that what is relevant is an assessment of ing in establishing guilt. A less idealized example arose in a the probability of an error resulting in an inappropriate match recent U.K. rape trial in which (by the admission of the declaration in the particular case at hand. These probabilities Downloaded by guest on September 26, 2021 Medical Sciences: Balding and Donnelly Proc. Natl. Acad. Sci. USA 92 (1995) 11745 will differ from case to case, depending, for example, on the Irrespective of any assessment of practical importance, it is details of sample collection and custody, possible replication of important as a matter of principle to ensure that presentations the analysis, and the times at which the crime and defendant of DNA evidence are fair to the defendant. sample were profiled. Nonetheless, the results of external, blind proficiency tests would appear extremely helpful in P.D. was supported in part by a Block grant from the University of forming a basis for appropriate assessments. Chicago and National Science Foundation Grant DMS-9505129. 6. Discussion 1. Collins, A. & Morton, N. E. (1994) Proc. Natl. Acad. Sci. USA 91, 6007-6011. 2. Balding, D. J. & Donnelly, P. (1996) J. Forensic Sci., in press. We do not propose that juries should be required to assess 3. Bernardo, J. M. & Smith, A. F. M. (1994) Bayesian Theory DNA identification evidence in terms of Eqs. 1 and 2. How- (Wiley, Chichester, U.K.). ever, a minimum requirement of a method for presenting DNA 4. Tillers, P. & Green, E., eds. (1988) Probability andInference in the evidence to be used in court is that concerns which arise as a Law of Evidence: The Limits and Uses of Bayesianism (Kluwer, consequence of the logical analysis are adequately addressed. Dordrecht, The Netherlands). Much current practice, based on reporting to. the court an 5. Aitken, C. G. G. (1995) Statistics and the Evaluation ofEvidence estimated profile frequency, does not satisfy this minimum for Forensic Scientists (Wiley, Chichester, U.K.). requirement. The profile frequency is not directly relevant and, 6. Evett, I. W. (1983) J. Forensic Sci. Soc. 23, 35-39. if viewed as an estimate of the match its 7. Koehler, J. J. (1993) Jurimetrics 34, 21-39. probability, implicit 8. Balding, D. J. & Donnelly, P. (October 1994) Crim. Law Rev., pp. assumption that the relevant correlations are zero is anticon- 711-721. servative, sometimes substantially so. Further, a juror told only 9. Balding, D. J. & Donnelly, P. (1995) J. R. Stat. Soc. A 158, 21-53. that the defendant has a profile which occurs in approximately 10. Evett, I. W. (1992) J. Forensic Sci. Soc. 32, 5-14. one in a million members of a population may immediately 11. Roeder, K. (1994) Stat. Sci. 9, 222-278. conclude that this is overwhelming evidence of the defendant's 12. Morton, N. E. (1992) Proc. Natl. Acad. Sci. USA 89, 2556-2560. guilt, irrespective of the other evidence even though, as 13. National Research Council (1992) DNA Technology in Forensic illustrated in Section 5.3, this information may in some cir- Science (Natl. Acad. Press, Washington, DC). cumstances be consistent with acquittal. More generally, we 14. Balding, D. J. & Nichols, R. A. (1995) Genetica 96, 3-12. 15. Balding, D. J. & Nichols, R. A. (1994) Forensic Sci. Int. 64, have argued that the hypothesis testing framework is not 125-140. appropriate for DNA evidence. 16. Morton, N. E., Collins, A. & Balazs, I. (1993) Proc. Natl. Acad. In many cases ajury may feel that the effect of the non-DNA Sci. USA 90, 1892-1896. evidence is at least to focus reasonable suspicion on the 17. Weir, B. S. (1994) Annu. Rev. Genet. 28, 597-621. defendant and away from her/his close relatives. In such cases 18. Cavalli-Sforza, L. L. & Piazza, A. (1993) Eur. J. Hum. Genet. 1, the additional effect of a four-locus match should be to make 3-18. the overall case against the defendant extremely strong. Nev- 19. Chakraborty; R., Srinivisan, M., Jin, L. & De Andrade, M. (1992) ertheless, in our experience there exists a substantial minority Proceedings of the Third International Symposium on Human Identification (Promega, Madison, WI), pp. 205-222. of cases in which the effects of the concerns raised here may 20. Li, C. C. & Chakravarti, A. (1994) Hum. Hered. 44, 100-109. be important. Examples include cases in which there is little or 21. Lander, E. S. & Budowle, B, (1994) Nature (London) 371, no evidence other than the DNA evidence, cases in which the 735-738. other evidence is exculpatory, and cases in which a partial or 22. Thompson, W. C. (1994) Stat. Sci. 9, 263-266. mixed profile is available or some experimental anomaly arises. 23. Dawid, A. P. & Mortera, J. (1996) J. R. Stat. Soc. B 58, in press. Downloaded by guest on September 26, 2021