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August 2021 A Problem in Forensic Science Highlighting the Differences between the Bayes Factor and Likelihood Ratio
Danica M. Ommen, Christopher P. Saunders
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Statist. Sci. 36(3): 344-359 (August 2021). DOI: 10.1214/20-STS805


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.

Funding Statement

Research supported by the National Institute of Justice, Office of Justice Programs, US Department of Justice under Award No. 2014-IJ-CX-K088. The opinions and conclusions or recommendations expressed in this presentation are those of the author and do not necessarily represent those of the Department of Justice.
The first author was supported in part by the Center for Statistics and Applications in Forensic Evidence (CSAFE) through Cooperative Agreement #70NANB15H176 between NIST and Iowa State University, which includes activities carried out at Carnegie Mellon University, University of California Irvine and University of Virginia.


We would like to thank our wonderful mentor Dr. JoAnn Buscaglia for the many helpful discussions throughout the years. Since the research presented in this article was performed as part of Dr. Ommen’s dissertation research at South Dakota State University, we would also like to thank the members of her departmental Ph.D. committee, Dr. Kurt Cogswell and Dr. Cedric Neumann, for their support and guidance. Finally, the authors are very grateful to Jakob Sohl and Jade Swanenburg from the Technical University of Delft for their careful technical review of our work and for noticing a mistake in the statement and proof of one of our theorems from an earlier version of this article. The interested reader (who reads Dutch) can find more detailed versions of the proofs of our theorems in Ms. Swanenburg’s Bachelor’s thesis [24].


Download Citation

Danica M. Ommen. Christopher P. Saunders. "A Problem in Forensic Science Highlighting the Differences between the Bayes Factor and Likelihood Ratio." Statist. Sci. 36 (3) 344 - 359, August 2021.


Published: August 2021
First available in Project Euclid: 28 July 2021

Digital Object Identifier: 10.1214/20-STS805

Keywords: Bayesian , common source , consistency , credible interval , forensics , frequentist , Model selection , specific source

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.36 • No. 3 • August 2021
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