Tutorial for Bayesian forensic likelihood ratio

TL;DR

This tutorial explains how to compute a Bayesian likelihood ratio for forensic evidence, integrating model uncertainty to produce a definitive value that aligns with intuitive expectations based on data quantity.

Contribution

It demonstrates a fully Bayesian approach to calculating likelihood ratios that accounts for model uncertainty and produces a single, sensible LR value.

Findings

The Bayesian LR aligns with common sense expectations.

Model uncertainty can be integrated out to produce a definitive LR.

The LR magnitude depends on the amount of data available.

Abstract

In the Bayesian paradigm for presenting forensic evidence to court, it is recommended that the weight of the evidence be summarized as a likelihood ratio (LR) between two opposing hypotheses of how the evidence could have been produced. Such LRs are necessarily based on probabilistic models, the parameters of which may be uncertain. It has been suggested by some authors that the value of the LR, being a function of the model parameters should therefore also be considered uncertain and that this uncertainty should be communicated to the court. In this tutorial, we consider a simple example of a 'fully Bayesian' solution, where model uncertainty is integrated out to produce a value for the LR which is not uncertain. We show that this solution agrees with common sense. In particular, the LR magnitude is a function of the amount of data that is available to estimate the model parameters.