9. Causal Inference*
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1.2. INDUCTIVE REASONING Much Mathematical Discovery Starts with Inductive Reasoning – the Process of Reaching General Conclus
1.2. INDUCTIVE REASONING Much mathematical discovery starts with inductive reasoning – the process of reaching general conclusions, called conjectures, through the examination of particular cases and the recognition of patterns. These conjectures are then more formally proved using deductive methods, which will be discussed in the next section. Below we look at three examples that use inductive reasoning. Number Patterns Suppose you had to predict the sixth number in the following sequence: 1, -3, 6, -10, 15, ? How would you proceed with such a question? The trick, it seems, is to discern a specific pattern in the given sequence of numbers. This kind of approach is a classic example of inductive reasoning. By identifying a rule that generates all five numbers in this sequence, your hope is to establish a pattern and be in a position to predict the sixth number with confidence. So can you do it? Try to work out this number before continuing. One fact is immediately clear: the numbers alternate sign from positive to negative. We thus expect the answer to be a negative number since it follows 15, a positive number. On closer inspection, we also realize that the difference between the magnitude (or absolute value) of successive numbers increases by 1 each time: 3 – 1 = 2 6 – 3 = 3 10 – 6 = 4 15 – 10 = 5 … We have then found the rule we sought for generating the next number in this sequence. The sixth number should be -21 since the difference between 15 and 21 is 6 and we had already determined that the answer should be negative. -
There Is No Pure Empirical Reasoning
There Is No Pure Empirical Reasoning 1. Empiricism and the Question of Empirical Reasons Empiricism may be defined as the view there is no a priori justification for any synthetic claim. Critics object that empiricism cannot account for all the kinds of knowledge we seem to possess, such as moral knowledge, metaphysical knowledge, mathematical knowledge, and modal knowledge.1 In some cases, empiricists try to account for these types of knowledge; in other cases, they shrug off the objections, happily concluding, for example, that there is no moral knowledge, or that there is no metaphysical knowledge.2 But empiricism cannot shrug off just any type of knowledge; to be minimally plausible, empiricism must, for example, at least be able to account for paradigm instances of empirical knowledge, including especially scientific knowledge. Empirical knowledge can be divided into three categories: (a) knowledge by direct observation; (b) knowledge that is deductively inferred from observations; and (c) knowledge that is non-deductively inferred from observations, including knowledge arrived at by induction and inference to the best explanation. Category (c) includes all scientific knowledge. This category is of particular import to empiricists, many of whom take scientific knowledge as a sort of paradigm for knowledge in general; indeed, this forms a central source of motivation for empiricism.3 Thus, if there is any kind of knowledge that empiricists need to be able to account for, it is knowledge of type (c). I use the term “empirical reasoning” to refer to the reasoning involved in acquiring this type of knowledge – that is, to any instance of reasoning in which (i) the premises are justified directly by observation, (ii) the reasoning is non- deductive, and (iii) the reasoning provides adequate justification for the conclusion. -
A Philosophical Treatise on the Connection of Scientific Reasoning
mathematics Review A Philosophical Treatise on the Connection of Scientific Reasoning with Fuzzy Logic Evangelos Athanassopoulos 1 and Michael Gr. Voskoglou 2,* 1 Independent Researcher, Giannakopoulou 39, 27300 Gastouni, Greece; [email protected] 2 Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, Greece * Correspondence: [email protected] Received: 4 May 2020; Accepted: 19 May 2020; Published:1 June 2020 Abstract: The present article studies the connection of scientific reasoning with fuzzy logic. Induction and deduction are the two main types of human reasoning. Although deduction is the basis of the scientific method, almost all the scientific progress (with pure mathematics being probably the unique exception) has its roots to inductive reasoning. Fuzzy logic gives to the disdainful by the classical/bivalent logic induction its proper place and importance as a fundamental component of the scientific reasoning. The error of induction is transferred to deductive reasoning through its premises. Consequently, although deduction is always a valid process, it is not an infallible method. Thus, there is a need of quantifying the degree of truth not only of the inductive, but also of the deductive arguments. In the former case, probability and statistics and of course fuzzy logic in cases of imprecision are the tools available for this purpose. In the latter case, the Bayesian probabilities play a dominant role. As many specialists argue nowadays, the whole science could be viewed as a Bayesian process. A timely example, concerning the validity of the viruses’ tests, is presented, illustrating the importance of the Bayesian processes for scientific reasoning. -
Judging the Evidence 2018 Contents World Cancer Research Fund Network 3 1
Judging the evidence 2018 Contents World Cancer Research Fund Network 3 1. Introduction 5 2. Randomised controlled trials 6 3. Epidemiological evidence 6 3.1 Cohort studies 9 3.2 Case-control studies 10 3.3 Other study designs 10 4. Meta-analysis 11 5. Experimental evidence 16 5.1 Human studies 16 5.2 Live animal models 16 5.3 In vitro studies 17 6. Methods of assessment 17 6.1 Foods, drinks and nutrients 17 6.2 Nutrition status 18 6.3 Physical activity 19 6.4 Cancer outcomes 20 7. Evidence collated for the Continuous Update Project 21 8. The grading criteria 22 8.1 Context for using the criteria 26 8.2 Food-based approach 27 8.3 CUP matrices 28 8.4 Levels and types of judgement 29 9. Conclusions 29 Acknowledgements 30 Abbreviations 34 Glossary 35 References 39 Our Cancer Prevention Recommendations 42 WORLD CANCER RESEARCH FUND NETWORK Our Vision We want to live in a world where no one develops a preventable cancer. Our Mission We champion the latest and most authoritative scientific research from around the world on cancer prevention and survival through diet, weight and physical activity, so that we can help people make informed choices to reduce their cancer risk. As a network, we influence policy at the highest level and are trusted advisors to governments and to other official bodies from around the world. Our Network World Cancer Research Fund International is a not-for-profit organisation that leads and unifies a network of cancer charities with a global reach, dedicated to the prevention of cancer through diet, weight and physical activity. -
Argument, Structure, and Credibility in Public Health Writing Donald Halstead Instructor and Director of Writing Programs Harvard TH Chan School of Public Heath
Argument, Structure, and Credibility in Public Health Writing Donald Halstead Instructor and Director of Writing Programs Harvard TH Chan School of Public Heath Some of the most important questions we face in public health include what policies we should follow, which programs and research should we fund, how and where we should intervene, and what our priorities should be in the face of overwhelming needs and scarce resources. These questions, like many others, are best decided on the basis of arguments, a word that has its roots in the Latin arguere, to make clear. Yet arguments themselves vary greatly in terms of their strength, accuracy, and validity. Furthermore, public health experts often disagree on matters of research, policy and practice, citing conflicting evidence and arriving at conflicting conclusions. As a result, critical readers, such as researchers, policymakers, journal editors and reviewers, approach arguments with considerable skepticism. After all, they are not going to change their programs, priorities, practices, research agendas or budgets without very solid evidence that it is necessary, feasible, and beneficial. This raises an important challenge for public health writers: How can you best make your case, in the face of so much conflicting evidence? To illustrate, let’s assume that you’ve been researching mother-to-child transmission (MTCT) of HIV in a sub-Saharan African country and have concluded that (claim) the country’s maternal programs for HIV counseling and infant nutrition should be integrated because (reasons) this would be more efficient in decreasing MTCT, improving child nutrition, and using scant resources efficiently. The evidence to back up your claim might consist of original research you have conducted that included program assessments and interviews with health workers in the field, your assessment of the other relevant research, the experiences of programs in other countries, and new WHO guidelines. -
Psychology 205, Revelle, Fall 2014 Research Methods in Psychology Mid-Term
Psychology 205, Revelle, Fall 2014 Research Methods in Psychology Mid-Term Name: ________________________________ 1. (2 points) What is the primary advantage of using the median instead of the mean as a measure of central tendency? It is less affected by outliers. 2. (2 points) Why is counterbalancing important in a within-subjects experiment? Ensuring that conditions are independent of order and of each other. This allows us to determine effect of each variable independently of the other variables. If conditions are related to order or to each other, we are unable to determine which variable is having an effect. Short answer: order effects. 3. (6 points) Define reliability and compare it to validity. Give an example of when a measure could be valid but not reliable. 2 points: Reliability is the consistency or dependability of a measurement technique. [“Getting the same result” was not accepted; it was too vague in that it did not specify the conditions (e.g., the same phenomenon) in which the same result was achieved.] 2 points: Validity is the extent to which a measurement procedure actually measures what it is intended to measure. 2 points: Example (from class) is a weight scale that gives a different result every time the same person stands on it repeatedly. Another example: a scale that actually measures hunger but has poor test-retest reliability. [Other examples were accepted.] 4. (4 points) A consumer research company wants to compare the “coverage” of two competing cell phone networks throughout Illinois. To do so fairly, they have decided that they will only compare survey data taken from customers who are all using the same cell phone model - one that is functional on both networks and has been newly released in the last 3 months. -
Could Low Grade Bacterial Infection Contribute to Low Back Pain? a Systematic Review
Urquhart et al. BMC Medicine (2015) 13:13 DOI 10.1186/s12916-015-0267-x RESEARCH ARTICLE Open Access Could low grade bacterial infection contribute to low back pain? A systematic review Donna M Urquhart1*, Yiliang Zheng1, Allen C Cheng1, Jeffrey V Rosenfeld2,3, Patrick Chan2,3, Susan Liew2,4, Sultana Monira Hussain1 and Flavia M Cicuttini1 Abstract Background: Recently, there has been both immense interest and controversy regarding a randomised, controlled trial which showed antibiotics to be effective in the treatment of chronic low back pain (disc herniation with Modic Type 1 change). While this research has the potential to result in a paradigm shift in the treatment of low back pain, several questions remain unanswered. This systematic review aims to address these questions by examining the role of bacteria in low back pain and the relationship between bacteria and Modic change. Methods: We conducted electronic searches of MEDLINE and EMBASE and included studies that examined the relationship between bacteria and back pain or Modic change. Studies were rated based on their methodological quality, a best-evidence synthesis was used to summarise the results, and Bradford Hill’s criteria were used to assess the evidence for causation. Results: Eleven studies were identified. The median (range) age and percentage of female participants was 44.7 (41–46.4) years and 41.5% (27–59%), respectively, and in 7 of the 11 studies participants were diagnosed with disc herniation. Nine studies examined the presence of bacteria in spinal disc material and all identified bacteria, with the pooled estimate of the proportion with positive samples being 34%. -
Building a Better Mousetrap: Patenting Biotechnology in the European
THE BRADFORD HILL CRITERIA: THE FORGOTTEN PREDICATE Dr. Frank C. Woodside, III* & Allison G. Davis** Table of Contents I. INTRODUCTION ....................................................................... 104 II. EPIDEMIOLOGY, DAUBERT, AND ESTABLISHING ASSOCIATION .................................................................... 107 A. Background on the Field of Epidemiology ...................... 107 B. Establishing Association .................................................. 108 C. Daubert and Its Progeny .................................................. 111 III. CAUSATION: THE NINE CRITERIA .................................... 112 A. Strength of Association ................................................... 113 B. Consistency ...................................................................... 114 C. Specificity of the Association .......................................... 116 * Frank C. Woodside, III is of counsel to the law firm of Dinsmore & Shohl. Dr. Woodside is a nationally-known trial lawyer representing manufacturers of pharmaceutical and medical devices, chemicals and flavorings, as well as producers of consumer products. Over a period of more than 40 years, he has tried 80-plus cases to verdict or judgment, serving as primary trial counsel in medical malpractice, product liability, and mass tort cases. Dr. Woodside’s clients include Fortune 500 companies, health care providers, and hospitals. His background to practice Medicine and Surgery for nearly 40 years affords him added knowledge and insight he uses to his -
The Problem of Induction
The Problem of Induction Gilbert Harman Department of Philosophy, Princeton University Sanjeev R. Kulkarni Department of Electrical Engineering, Princeton University July 19, 2005 The Problem The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not. So, for example, one valid deductive rule might be this: (D) From premises of the form “All F are G” and “a is F ,” the corresponding conclusion of the form “a is G” follows. The rule (D) is illustrated in the following depressing argument: (DA) All people are mortal. I am a person. So, I am mortal. The rule here is “valid” in the sense that there is no possible way in which premises satisfying the rule can be true without the corresponding conclusion also being true. A possible inductive rule might be this: (I) From premises of the form “Many many F s are known to be G,” “There are no known cases of F s that are not G,” and “a is F ,” the corresponding conclusion can be inferred of the form “a is G.” The rule (I) might be illustrated in the following “inductive argument.” (IA) Many many people are known to have been moral. There are no known cases of people who are not mortal. I am a person. So, I am mortal. 1 The rule (I) is not valid in the way that the deductive rule (D) is valid. The “premises” of the inductive inference (IA) could be true even though its “con- clusion” is not true. -
1 a Bayesian Analysis of Some Forms of Inductive Reasoning Evan Heit
1 A Bayesian Analysis of Some Forms of Inductive Reasoning Evan Heit University of Warwick In Rational Models of Cognition, M. Oaksford & N. Chater (Eds.), Oxford University Press, 248- 274, 1998. Please address correspondence to: Evan Heit Department of Psychology University of Warwick Coventry CV4 7AL, United Kingdom Phone: (024) 7652 3183 Email: [email protected] 2 One of our most important cognitive goals is prediction (Anderson, 1990, 1991; Billman & Heit, 1988; Heit, 1992; Ross & Murphy, 1996), and category-level information enables a rich set of predictions. For example, you might not be able to predict much about Peter until you are told that Peter is a goldfish, in which case you could predict that he will swim and he will eat fish food. Prediction is a basic element of a wide range of everyday tasks from problem solving to social interaction to motor control. This chapter, however, will focus on a narrower range of prediction phenomena, concerning how people evaluate inductive “syllogisms” or arguments such as the following example: Goldfish thrive in sunlight --------------------------- Tunas thrive in sunlight. (The information above the line is taken as a premise which is assumed to be true, then the task is to evaluate the likelihood of the conclusion, below the line.) Despite the apparent simplicity of this task, there are a variety of interesting phenomena that are associated with inductive arguments. Taken together, these phenomena reveal a great deal about what people know about categories and their properties, and about how people use their general knowledge of the world for reasoning. -
Does Sufficient Evidence Exist to Support a Causal Association Between Vitamin D Status and Cardiovascular Disease Risk?
Nutrients 2014, 6, 3403-3430; doi:10.3390/nu6093403 OPEN ACCESS nutrients ISSN 2072-6643 www.mdpi.com/journal/nutrients Review Does Sufficient Evidence Exist to Support a Causal Association between Vitamin D Status and Cardiovascular Disease Risk? An Assessment Using Hill’s Criteria for Causality Patricia G. Weyland 1,*, William B. Grant 2 and Jill Howie-Esquivel 1 1 Department of Physiological Nursing, School of Nursing, University of California, San Francisco (UCSF), #2 Koret Way Box 0610, San Francisco, CA 94143, USA; E-Mail: [email protected] 2 Sunlight, Nutrition, and Health Research Center, P.O. Box 641603, San Francisco, CA 94164-1603, USA; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +1-831-420-7324. Received: 22 May 2014; in revised form: 31 July 2014 / Accepted: 18 August 2014 / Published: 2 September 2014 Abstract: Serum 25-hydroxyvitamin D (25(OH)D) levels have been found to be inversely associated with both prevalent and incident cardiovascular disease (CVD) risk factors; dyslipidemia, hypertension and diabetes mellitus. This review looks for evidence of a causal association between low 25(OH)D levels and increased CVD risk. We evaluated journal articles in light of Hill’s criteria for causality in a biological system. The results of our assessment are as follows. Strength of association: many randomized controlled trials (RCTs), prospective and cross-sectional studies found statistically significant inverse associations between 25(OH)D levels and CVD risk factors. Consistency of observed association: most studies found statistically significant inverse associations between 25(OH)D levels and CVD risk factors in various populations, locations and circumstances. -
Bradford Hill Criteria for Causal Inference Based on a Presentation at the 2015 ANZEA Conference
Bradford Hill Criteria for Causal Inference Based on a presentation at the 2015 ANZEA Conference Julian King Director, Julian King & Associates – a member of the Kinnect Group www.julianking.co.nz | www.kinnect.co.nz 2015 We think we’re good at determining causality, but we suck at it One of the great At one level, this is an Unfortunately, though, the challenges in evaluation is everyday, common sense way we are wired does not determining whether the task. As a species we’ve predispose us to logical results we’re seeing are been making judgments thinking. We are inclined because of the program about causation for a to be led astray by all sorts we’re evaluating, some million years or so. of biases and heuristics. other influences out there in the big world, or random chance. The Kinnect Group www.kinnect.co.nz 2 Along came logic Eventually, after a very long time, we evolved into philosophers who invented formal logic. Thanks to scientific method, our species has recently triumphed to the extent that we now have cars that drive themselves and flying drones that deliver pizza (don’t confuse this with progress – we still suck at ethics but that’s a story for another day). 3 But we’re still not great at causation Over time, the rocket But deep down we’re still Such a rigid view is not science for dealing with biased, heuristical beings much use in the real causation has become and not very good at world, where there are all more sophisticated – a thinking things through.