Probabilistic Foundations for the use of the Logistic Regression Bayes Factor in Forensic Source Identification

• NCJ Number: 308217
• Author(s): Dylan Borchert
• Date Published: August 2023
• Length: 11 pages
• Agencies: NIJ-Sponsored
• Publication Type: Research (Applied/Empirical); Report (Grant Sponsored)

Annotation

This document is Travel Support Report for a poster presentation given at the 11th International Conference on Forensic Inference and Statistics (ICFIS) on the use of logistic regression (LR) Bayes Factor (BF) in forensic source identification.

Abstract

This paper reports on the contents of a poster presentation given at the 11th International Conference on Forensic Inference and Statistics (ICFIS) hosted in Lund, Sweden, on June 13, 2023. The authors present an approach to calculate Bayes factors (BFs) when using logistic regression as a model to discriminate between two classes. In comparison to likelihood ratios (LRs), BFs have the advantage that uncertainty in model parameter values is taken into account in a logical and coherent manner. In logistic regression, the log of the LR between the two classes follows a functional form. The authors focus on the case where this functional form is linear. This is equivalent to the log of the posterior odds of group membership following a linear model. Using a database of simulated observations generated under two different models, one can obtain a posterior distribution for the parameters of the logistic regression and use this distribution to obtain the posterior odds of group membership for a new observation with unknown membership. This posterior odds ratio can then be divided by the prior odds ratio to obtain the corresponding BF. The authors study the convergence of the BF to the LR for two different BF calculations and show that for large sample sizes they both converge. The authors also compare the calculated BFs of the two approaches to a reference BF, LR, and the plug-in estimate of the LR. The presenter of this work was funded by the National Justice Institute in the form of a Travel Grant to attend the ICFIS.