The DNA database search controversy revisited: Bridging the Bayesian - Frequentistic gap

Abstract

Two different quantities have been suggested for quantification of evidence in cases where a suspect is found by a search through a database of DNA profiles. The likelihood ratio, typically motivated from a Bayesian setting, is preferred by most experts in the field. The so-called $np$ rule has been suggested through more frequentistic arguments and has been suggested by i.e. American National Research Council and Stockmarr (1999). The two quantities differ substantially and have lead to what is called the DNA database search controversy. Although several authors have criticized the different approaches, a full explanation of why these differences appear is still lacking.

In this paper we show that a quantity approximately equal to the $np$ rule can be seen as a P-value in a frequentistic hypothesis setting. We argue however that a more reasonable procedure in this case is to use conditional testing, in which case a P-value directly related to posterior probabilities and the likelihood ratio is obtained. This way of viewing the problem bridge the gap between the Bayesian and frequentistic approaches. At the same time it indicates that the $np$ rule should not be used as a quantity of evidence.