Assessing forensic evidence by computing belief functions - theory and applications

We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We develop a new calculus of belief functions which does not use the much criticized Dempster rule of combination, and which yields very natural notions of conditioning and independence, consistent with their classical counterparts. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our setup can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.