Likelihood Ratio as Weight of Forensic Evidence: Whose Prior, Whose Likelihoods, and Whom Are We Kidding?

Abstract

Lindley (1979, Biometrika, pp 207-213) laid out a rational and coherent statistical framework to evaluate the weight of evidence in forensic science based on a subjective Bayesian modeling of the problem. The approach exploits the odds form of the Bayes rule which says ?????????????????????????????????? Posterior Odds = Prior Odds × Bayes Factor or, using the prevalent terminology among forensic scientists, ?????????????????????????????? Posterior Odds = Prior Odds × Likelihood Ratio. The idea is that the forensic expert will limit himself/herself to the calculation of the likelihood ratio (LR) and communicate the result to the court and the triers of fact (TOF) can modify their respective prior odds as to the guilt/innocence of the defendant by applying Bayes rule and arrive at their posterior odds. Thus, it appears that the assessment of the value of evidence by the forensic expert can be separated from subjective impressions regarding the guilt/innocence of the defendant. The approach is currently being evaluated as a candidate framework for adoption in the United States. Whereas the implementation of the Lindley framework appears to be straightforward, in practice it is fraught with challenges as it involves many subjective choices including choice of priors and of models. While any individual need only be satisfied with their own choices, the act of advising others as to how they may interpret avail- able information carries a greater burden in conveying, at each point, what choice was made and its effect relative to what other choices might have been made instead. In this talk we provide examples that illustrate how complex this process can be even in simple scenarios. In spite of this complexity, it is our view that the evidence interpreter has the responsibility to expend the necessary effort and tell the entire story behind any numerical summary such as the LR and, if justice is to be served, communicate as accurately as one can, the level of subjectivity and uncertainty accompanying such summaries. This is joint work with Steven P. Lund, NIST.