# 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 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=CurranTRANSCRIPT

<ul><li>1.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 </li></ul><p>2. 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 eect JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 2 / 48 3. JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48 4. JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48 5. JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48 6. JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48 7. JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 3 / 48 8. 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 9. 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 10. 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 11. 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 12. 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 Jeerson (Bill) Clinton (accused of having sexual relations with Monica Lewinsky) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 4 / 48 13. 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 14. 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 15. 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 16. 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 17. 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 18. 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 oers 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 19. Where does glass evidence come from? JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 7 / 48 20. Characterizing/quantifying glass evidence Colour, shape, density, refractive index, elemental composition JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 8 / 48 21. Measuring refractive index (RI) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 9 / 48 22. 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 23. Distribution of refractive index measurements (in NZ) JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 11 / 48 24. 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 25. Surface eects JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 13 / 48 26. Crown glass JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 14 / 48 27. An example On 3 March, 1991, a oat glass window was smashed in a pharmacy in Hamilton, New Zealand The oenders 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 28. The evidence Recovered from Johnstons clothing - small akes of paint - indistinguishable from crime scene - 11 fragments of glass MacKenzies clothing - 3 fragments of glass 3 fragments were original oat surfaces 9 control fragments taken from scene window Evidence quantied using RI JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 16 / 48 29. The evidence JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 17 / 48 30. 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 ) - 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 31. 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 Scientic interpretation is based on questions of the kind What is the probability of the evidence given the proposition? 3 Scientic 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 32. 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 33. A likelihood ratio for our case In the hierarchy of propositions the levels are oense, 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 34. 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 35. 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 36. 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 wasnt 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) nd 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 37. Multivariate glass evidence I have been discussing glass evidence measured on a single variable (RI) I will now talk briey 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. Specically 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 38. A LA-ICP-MS laboratory JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 26 / 48 39. A LA-ICP-MS laboratory JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 26 / 48 40. LA-ICP-MS at work A series of LA shots on a human hair A human hair is between 20 and 200 microns or 20 200 106 m wide JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 27 / 48 41. Statistical interpretation of elemental evidence Sequential comparison of recovered items to intervals dened 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 42. 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 aects 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 43. What does DNA evidence look like? RFLPs, VNTRs and autoradiographs Sir Alec Jereys ... 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 44. 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. Mulliss 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 45. What does DNA evidence look like? PCR + STRs: DNA proles what I see Thanks to IntergenX for the proles JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 32 / 48 46. What does DNA evidence look like? PCR + STRs: DNA proles what I see Thanks to IntergenX for the proles JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 32 / 48 47. What does DNA evidence look like? PCR + STRs: DNA proles what I see Thanks to IntergenX for the proles JM Curran (Statistics, Auckland) Forensic Statistics 2013-10-10 32 / 48 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 49. Did this blood come from that person? The oender 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 St...</p>