Title:

The effect of uncertainty about the background population on the forensic value of evidence

 

Presenter:

Dr. Christopher Saunders

Assistant Professor

Department of Mathematics and Statistics

South Dakota State University

 

January 18, 2013

4:00-5:00p.m.

MDS 220

 

Refreshments: 312 MDS building

3:30-4:00

 

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 inference usually concerns 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 randomly selected from a relevant alternative source population; i.e. the background population. The evidence that a forensic scientist is given for deciding between these two propositions is: (a) the trace of unknown origin, (b) a sample from the specific source specified by the prosecution hypothesis, and (c) a collection of samples from the alternative source population. One common approach is to assume that the collection of samples from the alternative source population is sufficiently large as to completely specify the alternative source population and to rely on a value of evidence for deciding between the competing hypotheses, as described in Lindley (1977). In this presentation, we present our construction of a Bayes Factor for deciding between the prosecution and defense hypotheses when the collection of samples from the alternative source population is not sufficiently large to completely characterize the alternative source population. We argue that the resulting Bayes Factor should be considered the Value of the Evidence and discuss its relationship to the standard value of evidence as developed by Lindley and presented in Aitken and Taroni (2004). We conclude with a discussion of some of our concerns about the effect of prior choice for the nuisance parameters in the alternative and specific source distributions on the resulting Bayes Factor. We will illustrate the construction of the Bayes Factors with a well-studied collection of samples relating to glass fragments under the assumption of a hierarchical normal model.