Why the effect of prior odds should accompany the likelihood ratio when reporting DNA evidence

Abstract

The introduction of DNA evidence has transformed human individualization in criminal litigation, butit also introduced daunting statistical, philosophical and practical problems into the process. The current practice in many legal cases is that a forensic expert reports a match probability or a likelihood ratio. However, the value of the likelihood ratio depends on the particular hypotheses used by the expert. Often there are various choices possible for the hypotheses used, and the corresponding likelihood ratios for different hypotheses are typically different.We therefore argue that the findings of an expert should not be given with a single number, and that any report with a match probability or likelihood ratio should be accompanied by a discussion of the effect of these numbers.We suggest away to do this, using the so-called posterior odds, which are invariant under various sets of hypotheses. Our approach is applicable in legal systems where the judge or jury is not allowed to know that the suspect was in a database. However, juridical problems may arise when courts insist on, for example, only a frequency estimate to be reported