Adventures in Forensic Statistics - James Curran
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Adventures in Forensic Statistics - James Curran

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Incredible developments in science and technology have given forensic scientists a powerful arsenal of tools for the detection, recovery, and quantification of evidence. Modern instrumentation can ...

Incredible developments in science and technology have given forensic scientists a powerful arsenal of tools for the detection, recovery, and quantification of evidence. Modern instrumentation can produce a DNA profile from a single human cell under ideal conditions, and from 5-6 cells under casework conditions. Similarly, current generation mass spectrometry equipment can detect differences in compounds in the parts per billion range. Quantifying evidence, however, is only one part of the legal process. The court wants to know “Does this piece of evidence make the defendant more likely to be guilty or innocent?” In order to answer this question we need statistics. All measurements have inherent variability, and where there is variability there is uncertainty and there are statisticians. In this talk I will explain the role of a statistician in forensic evidence interpretation and discuss some of the research questions that my collaborators and I have addressed over the last 20 years.

More information about Professor James Curran can be found at https://www.stat.auckland.ac.nz/showperson?firstname=James&surname=Curran

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    Adventures in Forensic Statistics - James Curran Adventures in Forensic Statistics - James Curran Presentation Transcript

    • Adventures in Forensic Statistics Professor James M. Curran Dept. of Statistics, University of Auckland 10th October 2013 JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 1 / 48
    • Forensic evidence ¢ Forensic evidence has been used in the courtroom for a very long time (take Sherlock Holmes for example) ¢ However it was not really until the late parts of the 20th century that the public really became aware of its power and usefulness ¢ This was mostly because of the advent of DNA evidence ¢ In the last few years forensic science has become glamorized due to the “CSI effect” JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 2 / 48
    • JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48
    • JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48
    • JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48
    • JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48
    • JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? Lindy Chamberlain (convicted and later acquitted of murdering daughter Azaria at Ayres Rock) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? David Bain (convicted and later acquitted of murdering his father, mother and sisters) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? Orenthal James (O.J.) Simpson (accused of murdering Nicole Brown Smith and Ron Goldman. Convicted of “wrongful death”) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? Orenthal James (O.J.) Simpson Convicted of armed robbery) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? William Jefferson (Bill) Clinton (accused of having “sexual relations” with Monica Lewinsky) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? Scott Watson (convicted of murdering Olivia Hope and Ben Smart) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? Joseph Thompson (South Auckland serial rapist) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? Malcolm Rewa (South Auckland serial rapist) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Major trials in NZ and around the world Think of some famous cases in New Zealand and around the world. Did they contain forensic evidence? What kind? Mark Lundy (convicted of murdering his wife and daughter) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48
    • Forensic evidence and the court ¢ People who are not forensic examiners (such as judges, lawyers and juries) often have trouble deciding whether a certain piece of evidence is important or relevant ¢ To address this problem, the court appoints experts to give their experienced opinion on the evidence ¢ However, generally an expert is not appointed independently. ¢ That is, the prosecution and defence hire experts whom they believe will strengthen their respective cases JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 5 / 48
    • What does the court want to know? The weight of the evidence “How much more likely (or less likely) does this evidence make it that the accused is guilty?” ¢ Statistics offers a framework in which evidence can be consistently evaluated ¢ That means that two experts who analyse the evidence in the same way will come up with the same statistic or conclusion ¢ It is for this reason alone that more and more judges and lawyers are demanding the use of statistics in conjunction with forensic evidence JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 6 / 48
    • Where does glass evidence come from? JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 7 / 48
    • Characterizing/quantifying glass evidence Colour, shape, density, refractive index, elemental composition JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 8 / 48
    • Measuring refractive index (RI) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 9 / 48
    • Measuring RI Silicone oil is heated until the optical density matches that of the glass. This (average) match temperature is converted into RI with a calibration line JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 10 / 48
    • Distribution of refractive index measurements (in NZ) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 11 / 48
    • Some useful questions ¢ Are pieces of glass from the same source more likely to be similar to each other than to glass from other sources? ¢ Is glass homogeneous within a source? JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 12 / 48
    • Surface effects JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 13 / 48
    • Crown glass JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 14 / 48
    • An example ¢ On 3 March, 1991, a float glass window was smashed in a pharmacy in Hamilton, New Zealand ¢ The offenders took drugs and prescription medicines worth thousands of dollars The suspects ¢ Police apprehended two suspects, Michael Johnston and John MacKenzie, 90 minutes later ¢ Their clothing was taken but the drugs were not found JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 15 / 48
    • The evidence ¢ Recovered from Johnston’s clothing - small flakes of paint - indistinguishable from crime scene - 11 fragments of glass ¢ MacKenzie’s clothing - 3 fragments of glass ¢ 3 fragments were original float surfaces ¢ 9 control fragments taken from scene window ¢ Evidence quantified using RI JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 16 / 48
    • The evidence JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 17 / 48
    • Match/non-match framework ¢ Very typical at the time of this case to use some criterion to determine whether the recovered measurements match the control measurements - Eyeballing - Range overlap tests (range or 2/3 σ) - t-test ¢ Johnston: t = 3.06, 19 df, P = 0.006 ¢ Mackenzie: t = 3.38, 10 df, P = 0.011 JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 18 / 48
    • Three principles of interpretation Evett and Weir (1998) proposed three basic principles of evidence interpretation 1 To evaluate the uncertainty of any given proposition it is necessary to consider at least one alternative proposition 2 Scientific interpretation is based on questions of the kind “What is the probability of the evidence given the proposition?” 3 Scientific interpretation is conditioned not only by the competing propositions, but also by the framework of circumstances within which they are to be evaluated JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 19 / 48
    • A likelihood ratio (LR) approach to evidence interpretation Many of my colleagues and I are proponents of what is called the “Bayesian,” or “LR,” or “logical” approach to evidence interpretation This way of thinking encapsulates all of the ideas on the previous slide We believe all forensic scientists should present evidence in the form of a likelihood ratio Odds form of Bayes’ Theorem Pr(Hp|Evidence) Pr(Hd |Evidence) Posterior Odds = Pr(Evidence|Hp) Pr(Evidence|Hd ) Likelihood Ratio × Pr(Hp) Pr(Hd ) Prior Odds JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 20 / 48
    • A likelihood ratio for our case ¢ In the hierarchy of propositions the levels are offense, activity and source (Cook et al., 1997) ¢ I will propose two competing hypotheses at the activity level ¢ These are: - Contact: The suspect was in contact with the crime scene - Contact: The suspect was not in contact with the crime scene ¢ To compute the LR I must assess the probability of the Evidence under each of these hypotheses JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 21 / 48
    • The LR under consideration ¢ The denominator of the LR is Pr(Evidence|Contact) = P1SLf ¢ This formula represents the probability of the evidence if the suspect was not at the crime scene ¢ If the suspect was not at the crime scene then the possible reason for presence of glass on his person might be - he had one group of glass from another source on his clothes - and it just happened to match the crime scene source by chance JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 22 / 48
    • The LR under consideration ¢ The numerator of the LR is Pr(Evidence|Contact) = TLP0 + T0P1SLf ¢ This formula represents the probability of the evidence if the suspect was at the crime scene ¢ If the suspect was at the crime scene then the possible reason for presence of glass on his person might - no glass was transferred from the scene - and he had one group of glass from another source on his clothes - and it just happened to match the crime scene source by chance OR - a large group of glass was transferred from the scene window - and he had no glass on his clothing from other sources JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 23 / 48
    • Interpretation of the LR ¢ Survey estimates give a likelihood ratio of 25 for Johnston and 10 for MacKenzie ¢ “The evidence is 25(10) times more likely if the suspect was at the crime scene than if he wasn’t” ¢ This method of interpretation gives a far more intuitive and usable result ¢ The disappointing truth is that most people (including the judge, the lawyers and the jury) find this statement incomprehensible ¢ These are examples of how this statement is incorrectly interpreted - “It is 25 times more likely that Johnston committed the crime” - “Johnston is 25 times more likely than anyone else to have committed the crime” JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 24 / 48
    • Multivariate glass evidence ¢ I have been discussing glass evidence measured on a single variable (RI) ¢ I will now talk briefly about glass evidence measured on many variables ¢ We have had the capability to analyse substances at an elemental level since the 1940s (NMR) ¢ These techniques have improved dramatically since then. Specifically they have become - very sensitive - elements can be measured in the low parts per billion range - non-destructive - laser ablation (LA) techniques mean that specimens are no longer destroyed - cheap(er) - a modern ICP-MS setup will cost around $US100,000 - down from $US500,000 JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 25 / 48
    • A LA-ICP-MS laboratory JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 26 / 48
    • A LA-ICP-MS laboratory JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 26 / 48
    • LA-ICP-MS at work A series of LA “shots” on a human hair A human hair is between 20 and 200 microns or 20 − 200 × 10−6 m wide JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 27 / 48
    • Statistical interpretation of elemental evidence Sequential comparison of recovered items to intervals defined by the control source Fe Mn Ba Sr Zr Cr Control Min. 1978 53 166 143 70 1494 Control Max. 2322 62 200 169 90 1771 Recovered 2320 62 192 166 99 1766 An example of a range test with elemental concentration data “Improvements” to this are using standard deviation, not range, and doing two-sample t-tests on an element-by-element basis JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 28 / 48
    • Dependency ¢ Probably the fundamental issue in evaluation of multivariate evidence is dependency ¢ This is common to both trace evidence and DNA evidence ¢ Dependency takes many forms and it affects the results in a variety of ways ¢ Correlation is one measure of dependency – but it is poorly understood JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 29 / 48
    • What does DNA evidence look like? RFLPs, VNTRs and autoradiographs Sir Alec Jeffreys ... had a “eureka moment” in his lab ... at 9:05 am on Monday 10 September 1984,... - [Wikipedia] JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 30 / 48
    • What does DNA evidence look like? PCR + Amplitype® Polymarker Kary Mullis (Nobel prize in Chemistry 1993) “Science has been just one of the keen interests in Dr. Mullis’s life, competing with psychedelic drugs and women” - Nicholas Wade, NY Times “...his only slides were photographs of his art which depicted naked women with colored lights projected on their bodies.” Kit available around 1992 JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 31 / 48
    • What does DNA evidence look like? PCR + STRs: DNA profiles – what I see Thanks to IntergenX for the profiles JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 32 / 48
    • What does DNA evidence look like? PCR + STRs: DNA profiles – what I see Thanks to IntergenX for the profiles JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 32 / 48
    • What does DNA evidence look like? PCR + STRs: DNA profiles – what I see Thanks to IntergenX for the profiles JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 32 / 48
    • The statistics of DNA evidence – a simple case ¢ A house is broken into and burgled ¢ Entry was gained by breaking a window and opening a door ¢ The burglar cut himself, leaving a blood stain ¢ Hours later the police apprehended a suspect (Curran) ¢ Suspect had a cut on his hand ¢ Suspect denies knowledge and involvement in the crime ¢ DNA sample taken from suspect matches the crime scene JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 33 / 48
    • Did this blood come from that person? ¢ The offender and the suspect have the same genetic type at this locus, i.e. the same genotype ¢ Does that mean the suspect is guilty? ¢ Forensic evidence can never answer this question directly. It can only make it more or less likely that it is true ¢ Forensic evidence can (usually) only address source level questions, not activity level questions JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 34 / 48
    • Why? Some questions you might ask yourself are: ¢ “How many other people have the same genotype?” ¢ “I inherited my DNA from my parents. Wouldn’t their types and those of my brothers and sisters be more similar than an unrelated person’s?” ¢ “What other reasons might there be for the presence of DNA?” JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 35 / 48
    • DNA profiles ¢ The questioned item has one or two alleles present at each locus ¢ If there is only a single contributor to the stain then there will be at most two alleles per locus ¢ The profiles are said to match or that the suspect cannot be excluded as a contributor of this item ¢ How do we assess this evidence statistically? ¢ One question people may ask is “How rare is this evidence?” or “How many people in the population have this profile?” ¢ This is something we can answer statistically with the population frequency of the profile JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 36 / 48
    • Population frequencies ¢ A traditional and commonly used approach is to calculate the frequency of the profile in the population ¢ This is the right answer to the wrong question ¢ Whilst the answer to this question may be interesting, it ignores one basic fact: we already know one person has this profile ¢ All probabilities are conditional We are interested in the answer to the following question: We know person X has this profile. What is the probability someone else has it? JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 37 / 48
    • Propositions What might the propositions be in our example case? Hp: the suspect (Curran) is the person who left this blood Hd : someone unrelated to the suspect left this blood Note these propositions are just that. Also they are not mutually exhaustive The probability of the evidence under Hp in this case is one. This reflects the idea that if the suspect did leave the blood then we expect to see his DNA profile (with certainty) How about the probability of the evidence under Hd ? We need a model JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 38 / 48
    • The defence proposition Under the defence hypothesis Hd we then must ask “What is the probability that someone else, other than the defendant, has this genotype?” To answer this question people often make some simplifying assumptions. These are: a. Independence of alleles within a locus (HWE) b. Independence of loci (LE) c. Independence of individuals in a population These are popular assumptions because most people remember that if events are independent then we can multiply However, most people also forget the “if events are independent” JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 39 / 48
    • Model assumptions – Hardy Weinberg Equilibrium For HWE to hold, a population must satisfy five conditions 1. Completely random mating – including selfing 2. No mutation 3. No migration 4. No selection 5. Infinite population size HWE cannot possibly be true in any human population JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 40 / 48
    • We cannot all be unrelated JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 41 / 48
    • The likelihood ratio (LR) in this case The LR (across all loci) using my profile, and the New Zealand Caucasian allele frequencies is 3.8 × 1013 Courtroom statement I would interpret this as: “The evidence is 3.8 × 1013 times more likely if the suspect was the donor rather than if someone unrelated to the suspect was the donor” Again, this is frequently misunderstood, misused, and misquoted JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 42 / 48
    • This statement is backwards JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 43 / 48
    • This statement is backwards JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 43 / 48
    • How do we (the jury) use this number? ¢ Assume we believed that the “odds on guilt” before we heard the DNA evidence were 1000 to 1 against ? i.e. we think it is a thousand time more likely that the suspect is innocent that guilty ¢ We can update these odds by multiplying by the LR ¢ E.g. the new odds are 3 × 1013 : 1 × 1 : 1000 = 3 × 1010 : 1 ¢ That is, it is 30 billion times more likely that the suspect (Curran) is the donor rather than someone unrelated to Curran (given the evidence) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 44 / 48
    • How do we (the jury) use this number? ¢ That is, after we heard the DNA evidence, we changed our beliefs from “leaning (strongly) towards innocence” to “very likely guilty than innocent” ¢ In practice, people rarely explicitly carry out this multiplication ¢ However, the thought process is the same: if the expert gives a big number they move towards guilt; if it is a small number (less than 1) they move towards innocence JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 45 / 48
    • Complicating the issues ¢ What if the alternative explanation is not that “the suspect is innocent and someone unrelated to him did it” but is “it wasn’t me it was my brother”? ¢ How about if the crime was a rape and the DNA evidence had a mixture of two people’s DNA (victim and rapist) or three people (victim, victim’s boyfriend and rapist). ¢ How do we come up with the values for the allele frequencies? Sampling? So is there a margin of error? JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 46 / 48
    • Relatedness and sampling uncertainty Balding and Nichols gave us a way of modelling departures from HWE pA|A = pA + (1 − pA)θ This quantity is greater than pA for any value of θ > 0. John Buckleton, Chris Triggs and I have done considerable research on: ¢ generalisations of calculations incorporating these effects ¢ the behaviour of the resulting estimators ¢ and the determination of appropriate values of θ for different populations. The last is extremely important because in general increasing θ decreases the LR We have also done considerable research into methodology for reflecting sampling uncertainty JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 47 / 48
    • Thanks I could not have done anything without the support and collaboration of: John Buckleton JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 48 / 48
    • Thanks I could not have done anything without the support and collaboration of: Chris Triggs JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 48 / 48
    • Thanks I could not have done anything without the support and collaboration of: Chris Triggs JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 48 / 48
    • Thanks I could not have done anything without the support and collaboration of: Bruce Weir JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 48 / 48
    • Thanks I could not have done anything without the support and collaboration of: Jo Ann Bright JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 48 / 48
    • Thanks I could not have done anything without the support and collaboration of: Family and friends JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 48 / 48