A Problem in Forensic Science Highlighting the Differences between the Bayes Factor and Likelihood Ratio

Abstract

This article is aimed at the growing number of statisticians interested in the important problem of interpreting evidence within the forensic identification of source problems. Our purpose is to formalize these forensic problems as statistical model selection problems. We use two different classes of statistics for quantifying the evidential value, the likelihood ratio and Bayes Factor. In forensics, both are commonly called the “likelihood ratio approach” and “the value of evidence” despite using different definitions of probability. In statistics, they are closely related to the traditional likelihood ratio from pattern recognition and the Bayes Factor used in model selection. For two different problem frameworks typical in forensic science, the common source and the specific source problems, we show the Bayes Factor and likelihood ratio are not equivalent, and highlight several interesting links between them. These contributions will help to elucidate the effects of choosing different definitions of probability when addressing the forensic identification of source problems. The broader population of statisticians may find this paper interesting as an introduction to forensic applications and for illuminating the connections between model selection methods from two different paradigms of statistics, particularly in view of the active recent discussions on the connections among Bayesian, Fiducial, Frequentist (BFF) approaches.