Abstract
The “rare type match problem” is the situation in which, in a criminal case, the suspect’s DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. Ideally, the evaluation of this observed match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) should be based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions and discards the information about the names of the different DNA profiles. This model is validated using data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to an Empirical Bayes approach for which we provided a motivation.
Highlights
The largely accepted method for evaluating how much some available data D helps discriminate between two hypotheses of interest is the calculation of the likelihood ratio (LR), a statistic that expresses the relative plausibility of the data under these hypotheses, defined as LR = Pr(D| H p ) Pr(D| Hd ) (1)Widely considered the most appropriate framework to report a measure of the ‘probative value’ of the evidence regarding the two hypotheses [1,2,3,4], it indicates the extent to which observed data support one hypothesis over the other
This model is validated using data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to an Empirical Bayes approach for which we provided a motivation
This paper proposes a first application of a Bayesian nonparametric method to assess the likelihood ratio in the rare type match case, the challenging situation in which there is a match between some characteristic of the recovered material and of the control material, but this characteristic has not been observed before in previously collected samples
Summary
The largely accepted method for evaluating how much some available data D (typically forensic evidence) helps discriminate between two hypotheses of interest (the prosecution hypothesis H p and the defense hypothesis Hd ) is the calculation of the likelihood ratio (LR), a statistic that expresses the relative plausibility of the data under these hypotheses, defined as LR = Pr(D| H p ) Pr(D| Hd ) (1). The likelihood ratio is supposed to be multiplied by the prior odds, in order to obtain the posterior odds. The latter is the quantity of interest for a judge, but the prior odds do not fall within the statistician’s competence. Even if a judge does not explicitly do Bayesian updating, the likelihood ratio is still considered to be the correct way for the expert to communicate their evaluation of the weight of the evidence to the court. Forensic literature presents many approaches to calculate the LR, mostly divided into Bayesian and frequentist methods
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