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

NCJ Number
Statistical Science Volume: 36 Issue: 3 Dated: August 2021 Pages: 344-359
Date Published
August 2021
16 pages

Intended for the increasing number of statisticians interested in the important problem of interpreting evidence within the forensic identification of source problems, this article formalizes these forensic problems as statistical model selection problems.


The project used 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, this work shows the Bayes Factor and likelihood ratio are not equivalent and highlights 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 article 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. (publisher abstract modified)

Date Published: August 1, 2021