Performance of likelihood ratios considering bounds on the probability of observing misleading evidence

Abstract

This is a pre-copyedited, author-produced version of an article accepted for publication in Law, Probability & Risk following peer review. The version of record Jose Juan Lucena-Molina, Daniel Ramos-Castro, Joaquin Gonzalez-Rodriguez; Performance of likelihood ratios considering bounds on the probability of observing misleading evidence. Law, Probability and Risk 2015; 14 (3): 175-192 is available online at: http://dx.doi.org/10.1093/lpr/mgu022In this article, we introduce a new tool, namely 'Limit Tippett Plots', to assess the performance of likelihood ratios in evidence evaluation including theoretical bounds on the probability of observing misleading evidence. To do that, we first review previous work about such bounds. Then we derive 'Limit Tippett Plots' that complements Tippett plots with information about the limits on the probability of observing misleading evidence, which are taken as a reference. Thus, a much richer way to measure performance of likelihood ratios is given. Finally, we present an experimental example in forensic automatic speaker recognition following the protocols of the Acoustics Laboratory of Guardia Civil, where it can be seen that 'Limit Tippett Plots' help to detect problems in the calculation of likelihood ratios