  The "rare type match problem" is the situation in which the suspect's DNA
profile, matching the DNA profile of the crime stain, is not in the database of
reference. The evaluation of this match in the light of the two competing
hypotheses (the crime stain has been left by the suspect or by another person)
is 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 fits very
well the data coming from European Y-STR DNA profiles, and the calculation of
the likelihood ratio becomes quite simple thanks to a justified Empirical Bayes
approach.
