The Evidential Value in the DNA Database Search Controversy and the Two-Stain Problem

Does the evidential strength of a DNA match depend on whether the suspect was identified through database search or through other evidence (“probable cause”)? In Balding and Donnelly (1995, Journal of the Royal Statistical Society, Series A158, 21–53) and elsewhere, it has been argued that the evidential strength is slightly larger in a database search case than in a probable cause case, while Stockmarr (1999, Biometrics55, 671–677) reached the opposite conclusion. Both these approaches use likelihood ratios. By making an excursion to a similar problem, the two-stain problem, we argue in this article that there are certain fundamental difficulties with the use of a likelihood ratio, which can be avoided by concentrating on the posterior odds. This approach helps resolving the above-mentioned conflict.