The evidential value in the DNA database search controversy and the two-stain problem

Summary . 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 A 158, 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 , Biometrics 55, 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.