Calculating the posterior odds from a single-match DNA database search

Forensic evidence is often quantified by statisticians in terms of a likelihood ratio. When the evidence consists of a DNA match, the likelihood ratio is equal to the reciprocal of the ‘random match probability’ (p). When p is small (e.g. 1/10 million), the likelihood ratio is large (e.g. 10 million to 1). However, when a single match is obtained by searching a database, the prior odds that the forensic DNA was deposited by the matcher can be extremely low, in which case the posterior odds can be low as well despite the high likelihood ratio. Unfortunately, prosecutors, judges and jurors are at risk of misinterpreting the likelihood ratio as the posterior odds, a pervasive reasoning error known as base-rate neglect. Here, we propose a solution to that problem, which consists of evaluating the prior odds based on a case-independent estimate of the size of the active criminal population derived from database search statistics. The posterior odds that the forensic DNA belongs to the unidentified single-matcher can then be calculated (avoiding base-rate neglect).