# A nonparametric Bayesian approach to the rare type match problem

## TL;DR

This paper introduces a Bayesian nonparametric method using a Poisson Dirichlet prior to address the rare type match problem in DNA analysis, simplifying likelihood ratio calculations when population proportions are unknown.

## Contribution

It presents a novel nonparametric Bayesian approach that models population proportions without relying on profile labels, improving analysis of rare DNA matches.

## Key findings

- Effective modeling of population proportions with Poisson Dirichlet distribution
- Simplified likelihood ratio computation via Empirical Bayes
- Well-suited for European Y-STR DNA profile data

## Abstract

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.