Bayesian Networks and the Value of the Evidence for the Forensic Two‐Trace Transfer Problem *

Abstract:  Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two‐trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two‐trace transfer problem and generalize this scenario to n traces.

[1]  F Taroni,et al.  The evaluation of evidence in the forensic investigation of fire incidents. Part II. Practical examples of the use of Bayesian networks. , 2005, Forensic science international.

[2]  F Taroni,et al.  A general approach to Bayesian networks for the interpretation of evidence. , 2004, Forensic science international.

[3]  Uffe Kjærulff,et al.  Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis , 2007, Information Science and Statistics.

[4]  Ian W. Evett.  A Quantitative Theory for Interpreting Transfer Evidence in Criminal Cases , 1984 .

[5]  Franco Taroni,et al.  Statistics and the Evaluation of Evidence for Forensic Scientists , 2004 .

[6]  Dw Van Boxel,et al.  Probabilistic Expert Systems for Forensic Inference from Genetic Markers , 2002 .

[7]  F Taroni,et al.  A probabilistic approach to the joint evaluation of firearm evidence and gunshot residues. , 2006, Forensic science international.

[8]  B. S. Weir.  DEOXYRIBONUCLEIC ACID | Statistical Analysis , 2000 .

[9]  H. D. De Kanter.  [The philosophy of statistics]. , 1972, Ginecología y Obstetricia de México.

[10]  Sally B. Mitchell,et al.  Encyclopedia of Forensic Science , 2004 .

[11]  R. Nichols,et al.  Interpreting DNA Evidence: Statistical Genetics for Forensic Scientists , 1999, Heredity.

[12]  A. Dawid,et al.  Probabilistic expert systems for DNA mixture profiling. , 2003, Theoretical population biology.

[13]  Colin Aitken,et al.  Analysis of sampling issues using Bayesian networks , 2007 .

[14]  I. Evett,et al.  More on the hierarchy of propositions: exploring the distinction between explanations and propositions. , 2000, Science & justice : journal of the Forensic Science Society.

[15]  Colin Aitken,et al.  Probabilistic reasoning in evidential assessment , 1989 .

[16]  Martin Neil,et al.  Building large-scale Bayesian networks , 2000, The Knowledge Engineering Review.

[17]  I. Evett,et al.  A hierarchy of propositions: deciding which level to address in casework , 1998 .

[18]  Ian W. Evett,et al.  On meaningful questions: a two-trace transfer problem , 1987 .

[19]  Avi Pfeffer,et al.  Object-Oriented Bayesian Networks , 1997, UAI.

[20]  C. Aitken,et al.  Statistics and the Evaluation of Evidence for Forensic Scientists: Aitken/Statistics and the Evaluation of Evidence for Forensic Scientists , 2005 .

[21]  J Mortera,et al.  Object-oriented Bayesian networks for complex forensic DNA profiling problems. , 2007, Forensic science international.

[22]  A. Philip Dawid,et al.  USING A GRAPHICAL METHOD TO ASSIST THE EVALUATION OF COMPLICATED PATTERNS OF EVIDENCE , 1997 .

[23]  Colin Aitken,et al.  Bayesian Networks and Probabilistic Inference in Forensic Science , 2006 .

[24]  Finn V. Jensen,et al.  Bayesian Networks and Decision Graphs , 2001, Statistics for Engineering and Information Science.

[25]  C M Triggs,et al.  The two trace transfer problem re-examined. , 2003, Science & justice : journal of the Forensic Science Society.

[26]  L Nyström,et al.  Statistical Analysis , 2008, Encyclopedia of Social Network Analysis and Mining.

[27]  A. P. Dawid.  Which likelihood ratio? (Comment on ‘Why the effect of prior odds should accompany the likelihood ratio when reporting DNA evidence’, by Ronald Meester and Marjan Sjerps) , 2004 .

[28]  F Taroni,et al.  The evaluation of evidence in the forensic investigation of fire incidents (Part I): an approach using Bayesian networks. , 2005, Forensic science international.

[29]  Amanda B. Hepler,et al.  Object-Oriented Graphical Representations of Complex Patterns of Evidence , 2007 .