Statistics and Probability in Forensic Anthropology provides a practical guide for forensic scientists, primarily anthropologists and pathologists, on how to design studies, how to choose and apply statistical approaches, and how to interpret statistical outcomes in the forensic practice. But there is no way for the forensic scientist to reach such conclusions based on the forensic findings alone. In an effort to being to understand and move beyond the innumeracy present in the law, I distinguish between two types of innumeracy by lawyers: objective innumeracy (or a lack of math competence) and subjective innumeracy (or a lack of math confidence) and suggest that empirical research into the causes of legal innumeracy is needed. No use, distribution or reproduction is permitted which does not comply with these terms. By applying this method, factfinders should try — and will often succeed — to establish the truth, rather than a statistical surrogate of the truth, while securing the appropriate allocation of the risk of error. The importance of math in the administration of justice has risen with the growth of identification forensics and its influence continues to permeate questions of proof and judgment. These include some form of circumscribed and standardized testimony. 1955).”, People v. Collins, 68 Cal. The gravamen of the error came during the trial judge’s comment construing the testimony in terms of the probability of making an erroneous identification through the comparison of hair samples. Crim Law Rev 5:347-356 Google Scholar Robertson B, Vignaux GA (1995) Interpreting evidence. Bayes' rule specifies how one ought to combine prior probabilities with the results of a DNA profiling analysis in order to find the so-called posterior probabilities that the defendant is the source of the blood. A bayesian approach to identification evidence. Use of prior odds for missing persons identifications. at 759 (“In this category, empirical statistics form part of the basis for formation of a subjective probability, but not via use of Bayes’ Theorem (e.g., “Based upon my assessment of the probability of truth of the eyewitness testimony plus the statistics regarding blood factors, I believe that the defendant’s guilt is extremely probable.”)”). The Numbers Guy (Wall St. Instead, it has sold 4 million, in 35 languages. Treatment of inconclusives in the AFTE range of conclusions, Coherently updating degrees of belief: Radical Probabilism, the generalization of Bayes’ Theorem and its consequences on evidence evaluation, Mt. While the jury apparently did not credit this evidence, it cannot be ignored in evaluating whether there was a substantial risk of a miscarriage of justice.”, Dorsey v. State, 350 A. This curriculum is designed to provide knowledge of forensic science systems and operations: Study will focus on local, state, and federal law enforcement, evidence processing and procedures. .We believe that testimony to statistical probabilities encouraged the jury to disregard evidential risks traditionally weighed in determining guilt or innocence, and focused unfairly upon a numerical conclusion. If forensic scientists will make the ultimate determination, for legal purposes, with regard to a particular proposition of interest, then they should, and indeed must, consider their prior probabilities that the hypotheses are true. Primer for the Nonmathematically Inclined on Mathematical Evidence in Criminal Cases: People v. Collins and Beyond, Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach, Probability, Individualization, and Uniqueness in Forensic Science Evidence: Listening to the Academies, Scientifically Trained Law Clerk: Legal and Ethical Considerations of Relying on Extra-Record Technical Training or Experience, Trial by Mathematics: Precision and Ritual in the Legal Process, Community Detection Using Spectral Clustering on Sparse Geosocial Data, Forensic Due Process: Lawyering With Science, Letter to the Editor: An Application of Mathematics to Law. .Permitting the detective to relate syllogistically — though imperfectly — before the jury, the high probability of the appellant’s guilt, tended to portray the officer as a ‘super-investigator’ and thus clothed his testimony, with a greater weight than that which might have been given to the testimony of the other witnesses. The single cigarette butt that allegedly had appellant’s DNA on it did nothing more than place appellant in Larson’s Danville apartment at some unknown time. Starting from its roots and reviewing its progress to the present day, it is argued that while the science which supports statistical evidence has become ever more sophisticated, almost nothing has changed in English courts so far as what happens during the process of a trial. indict. In short, there is no foundation upon which to base his probabilities of one in a million.‘An expert witness’ view as to probabilities is often helpful in the determination of questions involving matters of science or technical or skilled knowledge. Ct. 2011)“We conclude that the prosecutor’s closing argument error created a substantial risk of a miscarriage of justice because of the danger that the jury gave undue weight to a mathematical probability analysis that supposedly demonstrated that the lone eyewitness identification on which the prosecutor’s case wholly rested constituted proof beyond a reasonable doubt, the victim’s admitted uncertainty as to the accuracy of the identification, and our recognition that “[e]yewitness identification of a person whom the witness had never seen before the crime or other incident presents a substantial risk of misidentification and increases the chance of a conviction of an innocent defendant.” Commonwealth v. Silva-Santiago, 453 Mass. The extant burden-of–proof doctrine, we conclude, works well and requires no far-reaching reforms.”, Further Critique of Mathematical Proof, 84 Harv. While the jury can take the other evidence into account they may have difficulty integrating it with the “probability of paternity” delivered by the forensic expert, or they may mistakenly assume that the “probability of paternity” is all they need consider. Whether forensic scientists should take account of the prior probability of the hypotheses they are asked to help evaluate is a complicated question. But the Bayesian approach will only work if the expert can begin with a prior probability. Anybody who has inspected datasets with the purpose of using them as elementary examples knows that this is hard: on the one hand, you do not want to boldly state assumptions that are clearly not satisfied; on the other hand, long explanations concerning side issues distract from the main points. Thus, the jury’s basic function of weighing the conflicting evidence in arriving at a conclusion of guilt ‘beyond a reasonable doubt,’ was subjected to the counterbalancing effect of the detective’s irrelevant and extraneous opinion. With respect to the statistical evidence, Supreme Court admonished the jury that the opinions expressed by the expert were based upon a number of assumptions and judgments that the jury had to accept before it could consider the expert’s mathematical calculations. 2d 319 (Sup. 781, 787-788 (Mass. Matthews had made no tests on which he could reasonably base his probabilities of one in ten on soil color, one in one hundred on soil texture, or one in one thousand on soil density (which he multiplied together to obtain his one-in-one-million figure), nor did he base his testimony on studies of such tests made by others. To devise methods that have no practical purpose – and whose validity cannot be empirically tested – but that serve only to advance understanding – possibly contemplative understanding – of the nature of inconclusive argument about uncertain factual hypotheses in legal settings.”, Use of Statistics in Criminalistics. .We conclude, as did the Court of Special Appeals, that the collateral evidence elicited from Detective Simmons, concerning his arrest-conviction record, was irrelevant and extraneous to the issue of the appellant’s guilt or innocence, and that the trial court’s ruling, permitting it, was manifestly erroneous.”, Meredith v. A.3 The Weight of Evidence 190. This is sometimes described as a position of neutrality and is often justified with references to vague accessory “principles,” such as the “Principle of Indifference” or the “Principle of Maximum Entropy,” borrowed from other disciplines and contexts (Biedermann et al., 2007). Under the circumstances, the expert testimony did not invade “`the jury’s exclusive province of determining an ultimate fact issue in the case'” (People v Bajraktari, 154 AD2d 542, 543, lv denied 75 N.Y.2d 963, quoting People v Abreu, 114 AD2d 853, 854).”, State v. Carlson, 267 NW 2d 170 (Minn. Sup. He defined the law of probabilities as ‘A proper fraction expressing the ratio of the number of ways an event may happen divided by the total number of ways in which it can happen.’ The various defects claimed to be visible and pointed out by the experts in the specimens of typewriting made upon the defendant’s machine corresponding to like defects in the letters of the two words ‘the same’ in the alleged altered document were called to the witness’ attention by the district attorney, and he was asked to apply the law of mathematical probability thereto. doi: 10.1186/2041-2223-3-2, Budowle, B., Ge, J., Chakraborty, R., and Gill-King, H. (2011). 3. 514 (1964)“This paper will present a relatively non-technical discussion of some aspects of the utilization of statistics in the field of criminalistics. A colorful narrative of mathematical abuse, Math on Trial blends courtroom drama, history, and math to show that legal expertise isn’t always enough to prove a person innocent.”, Modern Introduction to Probability and Statistics: Understanding Why and How (Springer 2005)“In this book you will find the basics of probability theory and statistics. It also offers recommendations and additional strategies that investigators may find helpful.”, Evidence: Admission of Mathematical Probability Statistics Held Erroneous for Want of Demonstration of Validity, 1967 Duke L.J. Keywords: DNA, Bayes Theorem, prior probability, expert testimony, forensic science, Citation: Thompson WC, Vuille J, Biedermann A and Taroni F (2013) The role of prior probability in forensic assessments. In light of Strauss’ testimony, we regard Gaudette’s statement as cumulative and thus nonprejudicial on the facts of this case.”, State v. Hernandez, 531 NW 2d 348 (Wis. Ct. App. An example is a forensic "star" that attested in various lawsuits and faked test outcomes. (forthcoming 2013)“This Article analyzes the probabilistic and epistemological underpinnings of the burden of proof doctrine. Thank you very much. For example, coroners are sometimes given full responsibility for determining the cause and manner of a death for legal purpose. It is hoped that this presentation will help to orient the reader toward a better understanding of the proper role of statistical methods in criminalistics.” CURRENT AWARENESS, Forensic Mathematics (Charles H. Brenner, Ph.D.)“Forensic Mathematics… is the best short description that I have found to describe the work that I do, which mostly pertains to DNA identification, and includes consulting, writing software – DNA*VIEW is used by some 100 laboratories, in every continent (except Antarctica) – academic activities in mathematics, biostatistics, and various aspects of population genetics.”. Genet. I t's not often that the quiet world of mathematics is rocked by a murder case. Individuality implies that every entity, whether person or object, can only be identical to itself and so is unique. For the most part the evidence to be evaluated will be so-called transfer or trace evidence. an azoospermic cosmonaut) is treated the same as any other man. Index 193 The witness asserted that when the facts are ascertained, the application of the law of probabilities to them is a matter of pure mathematics and not of speculation or opinion. From forensics to counterterrorism, the Riemann hypothesis to image enhancement, solving murders to beating casinos, Devlin and Lorden present compelling cases that illustrate how advanced mathematics can be used in state-of-the-art criminal investigations.”, Principles and Practices for a Federal Statistical Agency (5th ed. See State v. Wolff, 171 Wis. 2d 161, 168, 491 N.W.2d 498, 501 (Ct. App. 57 (1970-1971)“In this article I [Robert L. Birmingham] attempt to use the techniques of game theory to isolate minimal attributes of problems familiar in criminal law. Recognizing that these situations are unusual, however, it also surveys some evidentiary rules and practices that could curb the excesses of the current form of testimony.”, Scientifically Trained Law Clerk: Legal and Ethical Considerations of Relying on Extra-Record Technical Training or Experience, ExpressO (2013)“Technically trained law clerks should be permitted to rely on extralegal scientific principles, but only if those principles are objectively verifiable and not subject to reasonable dispute—a standard that matches Federal Rule of Evidence 201. We substantiate this claim by juxtaposing the extant doctrine against two recent contributions to evidence theory: Professor Louis Kaplow’s proposal that the burden of proof should be modified to track the statistical distributions of harms and benefits associated with relevant primary activities; and Professor Edward Cheng’s model that calls on factfinders to make their decisions by using numbers instead of words. During the study period, the two halves differed significantly in racial makeup — the population of North County was over 30% African-American, and of South County less than 5% African-American; and the two halves differed in the race of homicide victims — in North County, African-Americans were homicide victims roughly 4.5 times as often as Whites, while, in South County, Whites were homicide victims more than three times as often as African-Americans. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). It did not limit appellant’s presence to the weekend before her disappearance. On a practical level, we miscalculate numbers, oversimplify formulas, and, ultimately, misapply mathematical principles. In any event, defendant was not thereby deprived of a fair trial. Table 1 shows how this is done. 2d 319 (Sup. 343 (1986)“This article examines the confusion that can confound courts in understanding a certain kind of probability (called a P-value) that can be helpful in evaluating the significance of statistical evidence in criminal trials, particularly when it is used as a measure of the probative value of identification evidence – things like bloodstains, hair fibers, fingerprints and forged documents. Jurors are carefully chosen for the task, are often shielded by evidentiary rules from information that the legal system determines that they should not consider, and are carefully instructed on the presumptions to make and standards to apply in reaching a verdict; experts are not. The jurors might want the expert to tell them definitively which hypothesis is true, or to give them particular values for the so-called source probabilities—saying, for example, that there is a 0.998 probability the defendant is the source of the blood and only a probability of 0.002 that someone else was the source. At the same time, the author suggested that there are circumstances in which “probability evidence” should be admissible, and promised to chart a middle course between Procrustean exclusion of probability evidence and uncritical acceptance of numerobabble. For example, statistics (evidence) and probability (analytics) 1 have been used and . By clarifying the relationship between uniqueness and individualization, the essay advances a slightly less skeptical view of individualization than that expounded by Professors Michael Saks and Jay Koehler. In order to assign prior contextually meaningful probabilities, the expert would need to take into account all of the evidence in the case. For example, statistics (evidence) and probability (analytics)1 have been used and challenged in many criminal cases to match people to events through such means as: DNA, soil samples, eyewitness descriptions, firearm purchase records, typewritten documents, clothes fibers, footprints, hair follicles, blood types, sperm, teeth marks, and conviction rates.2 Indeed, everything from traffic tickets to predictive policing draws on math in some way.3, Nonetheless, legal reasoning has on occasion too quickly arrogated mathematical logic resulting in arguments based on fallacies and confusion.4 It is a subject that has been debated periodically in the history of law and tests the integrity of legal decision-making in many areas that rely on numerical interpretations of human policies and actions.5, David McCord, Professor of Law, Drake University Law School, observed that the legal literature on this subject tends to categorize precedent along legal and not mathematical lines, further impeding a consistent approach to this type of proof or analysis.6 In order to clarify these forensic applications, Prof. McCord outlined five distinct areas of mathematical evidence: (1) “empirical statistics”;7 (2) “probabilities of a random match”; 8 (3) “nonempirical probabilities of guilt incorporating empirical statistics without Bayes’ Theorem”;9 (4) “non-empirical probabilities of guilt developed without empirical statistics and without Bayes’ Theorem”;10 and (5) “non-empirical probabilities of guilt incorporating empirical statistics via Bayes’ Theorem.”11. For example, what is the probability that a nylon fiber originated from a particular sweater, or that a paint chip came from a suspect car in a hit and run? Copyright © 2013 Thompson, Vuille, Biedermann and Taroni. Based on this assessment the expert might also provide to the jury a so-called likelihood ratio—saying, for example, that the DNA profiling results are 1 million times more probable if the defendant rather than some other person was the source of the blood. Allegedly incriminating audio clips may become viral on social media, give political mileage and create a media sensation, but may not be sufficient to nail a suspect. Indeed in the absence of any showing of similarity between the investigation which led to the appellant’s arrest and those other investigations which led to the detective’s conviction rate, the premise posited before the jury appears to have been invalid. 160 (1987)“Part I of this article described some classic cases in which dubious testimony about probabilities helped convict defendants. There is a well-known principle in forensic science known as Locard's . Some courts oppose this probability evidence completely, while others uncritically admit it, thus exposing the need for a middle road.”, Admissibility of ‘Probability Evidence’ in Criminal Trials – Part II, 27 Jurimetrics J. A forensic scientist is asked to perform DNA profiling analyses of blood found at a crime scene and to compare the result to the DNA profile of a defendant who is charged with the crime. DM = Prior Odds. For example, lawyers might be able to improve the way they instruct experts and lead their evidence in court by gaining insight into forensic scientists' thinking about probability and statistics; whilst forensic scientists, for their part, may become more proficient as expert witnesses by The law's use of the word "reliably" to connote probable factual accuracy is potentially confusing, since "reliability" has a distinct meaning in statistical science. J. . 84 Harv. He should not be confused with the medical examiner, who merely provides information to a court in the course of criminal prosecution or civil litigation but has no judicial authority of his own). Improper use of Forensic Science in the First 200 Post-Conviction DNA Exonerations Brandon L. Garrett, Associate Professor of Law, University of Virginia Peter Neufeld, Co-Founder and Co-Director, The Innocence Project Preliminary data for study in progress; do not cite or distribute without permission of authors Presented in this paper are arguments that studies of evidence in the fields of law and probability constitute a science of evidence when they are examined in light of five criteria for scientific activity. Behav. This article discusses a series of related propositions about criminal cases that include “trace evidence” – bloodstains, semen, glass fragments, fibers, or other materials – linking a defendant to a crime. Disputes about this issue have arisen in a number of contexts and recent examples suggest that opinions still diverge (e.g., Budowle et al., 2011; Biedermann et al., 2012). Then they wrote SuperFreakonomics, with stories about drunk walking, the economics of prostitution, and how to stop global warming. Please click the Donate button and support LLRX. First, the expert’s testimony was later ordered stricken from the record after Hernandez was able to get the expert to admit that she had no foundation for her one percent opinion. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. Describes ways of assessing forensic science evidence and the means of communicating the assessment to a court of law. The expert answered, “I had a case where there was fabrication, Yes.” On redirect examination, the prosecutor asked the expert whether she was aware of any percentages about how many cases are fabricated. 1166 [Vol. Finally we analyze the robustness of this technique with respect to noisy and incomplete data, thereby providing suggestions about the relative importance of quantity versus quality of collected data.”). As a profession, in the 21 st century, it has taken root in today's society though with different levels of advancement, protocols and policies in different jurisdictions. The witness, so far as the record discloses, was not qualified as an expert in typewriting; he had never made a study of such work, or of the machine claimed to have been used for the purpose of interpolating words in the document offered in evidence, nor did he take into consideration in arriving at his result the effect of the human operation of such a machine, that is whether the same defects would always be discernible, no matter who was the individual operating the machine. The only coherent way to draw conclusions about source probabilities on the basis of forensic evidence is to apply Bayes' rule, which requires that one begins with an assignment of prior probabilities to the propositions of interest (e.g., Robertson and Vignaux, 1995; Finkelstein and Fairley, 1970). A committee of the National Academy of Sciences, building on the writing of academic commentators, has called for sweeping changes in the presentation and production of evidence of identification. Michael O. Finkelstein and Professor William B. Fairley, authors of a proposal challenged by Professor Tribe, here respond to defend both their own technique and the use of mathematics at trial generally; Professor Tribe, in turn, replies with a further criticism of mathematical proof. Redmayne M, Roberts P, Aitken CGG, Jackson G (2011) Forensic science evidence in question. 211-302); Reference Guide on Multiple Regression (pp. It provides the possibility to derive confidence intervals and perform tests of hypotheses where traditional (normal approximation or large sample) methods are inappropriate. 1329 (1971)“Professor Tribe considers the accuracy, appropriateness, and possible dangers of utilizing mathematical methods in the legal process, first in the actual conduct of civil and criminal trials, and then in designing procedures for the trial system as a whole. To predict how judges and jurors will resolve factual issues in litigation. at 758 n. 1995)“Hernandez has one further complaint about the expert. 69. 11 Id. In particular, the bootstrap has earned its place. 2013)“Publicly available statistics from government agencies that are credible, relevant, accurate, and timely are essential for policy makers, individuals, households, businesses, academic institutions, and other organizations to make informed decisions. This paper uses a likelihood ratio (LR) approach to identify the probative value of forensic science evidence. 2011); Admissibility, in Criminal Case, of Statistical or Mathematical Evidence Offered for Purpose of Showing Probabilities, 36 A.L.R.3d 1194. After discussing basic probability concepts, he outlines an extensive probabilistic model for analyzing the judicial factfinding process. The author maintains that reasonable estimates of pertinent population proportions should be admissible, that argument on the part of counsel as to corresponding estimates of the probability of a coincidental misidentification should be permitted, and that neither expert opinions as to whether the defendant left the trace evidence nor displays of the posterior probability that defendant did so should be admissible.”, Amoral Numbers and Narcotics Sentencing, Val. Probability has its origin in the study of gambling and insurance in the 17th century, and it is now an indispensable tool of both social and natural sciences. Finally, and most worryingly, our findings show that the substance of legal analysis varies with math skill for at least some subset of cases.”, People v. Nelson: A Tale of Two Statistics, 7 Law Probability & Risk 249 (2008)“In recent years, defendants who were identified as a result of a search through a database of DNA profiles have argued that the probability that a randomly selected person would match a crime-scene stain overstates the probative value of the match.