A Note on the Specific Source Identification Problem in Forensic Science in the Presence of Uncertainty about the Background Population

Abstract

A goal in the forensic interpretation of scientific evidence is to make an inference about the source of a trace of unknown origin. The evidence is composed of the following three elements: (a) the trace of unknown origin, (b) a sample from a specific source, and (c) a collection of samples from the alternative source population. The inference process usually considers two propositions. The first proposition is usually referred to as the prosecution hypothesis and states that a given specific source is the actual source of the trace of unknown origin. The second, usually referred to as the defense hypothesis, states that the actual source of the trace of unknown origin is another source from a relevant alternative source population. One approach is to calculate a Bayes Factor for deciding between the two competing hypotheses. This approach commonly assumes that the alternative source population is completely known or uses point estimates for its parameters. Contrary to this common approach, we propose a development that incorporates the uncertainty on the alternative source population parameters in a reasonable and coherent manner into the Bayes Factor. We will illustrate the resulting effects on the calculation of several Bayes Factors for different situations with a well-studied collection of samples of glass fragments.