Bayesian Reasoning and Evidence Communication

TL;DR

This paper clarifies how Bayesian reasoning should guide the updating of personal uncertainty when receiving likelihood ratios from experts, emphasizing that hybrid methods deviate from proper Bayesian updating and discussing implications for forensic testimony.

Contribution

It demonstrates that the common hybrid approach to updating beliefs with likelihood ratios is inconsistent with Bayesian principles and explores the implications for expert evidence communication.

Findings

Hybrid likelihood ratio updates are not Bayesian

Proper Bayesian updating involves personal prior and likelihoods

Implications for forensic testimony and expert reports

Abstract

Many resources for forensic scholars and practitioners, such as journal articles, guidance documents, and textbooks, address how to make a value of evidence assessment in the form of a likelihood ratio (LR) when deciding between two competing propositions. These texts often describe experts presenting their LR values to other parties in the judicial system, such as lawyers, judges, and potentially jurors, but few texts explicitly address how a recipient is expected to utilize the provided LR value. Those that do often imply, or directly suggest, a hybrid modification of Bayes' rule in which a decision maker multiplies their prior odds with another person's assessment of LR to obtain their posterior odds. In this paper, we illustrate how someone adhering to Bayesian reasoning would update their personal uncertainty in response to someone else presenting a personal LR value (or any other form of an opinion) and emphasize that the hybrid approach is a departure from Bayesian reasoning. We further consider implications of recipients adhering to Bayesian reasoning on the role and ideal content of expert's reports and testimony and address published responses to our 2017 paper (Lund and Iyer, 2017), where we previously argued that the hybrid equation is not supported by Bayesian reasoning.