Exact computation of the distribution of likelihood ratios with forensic applications

Abstract

If complex DNA profiles, conditioned on multiple individuals are evaluated, it may be difficult to assess the strength of the evidence based on the likelihood ratio. A likelihood ratio does not give information about the relative weights that are provided by separate contributors. Alternatively, the observed likelihood ratio can be evaluated with respect to the distribution of the likelihood ratio under the defense hypothesis. We present an efficient algorithm to compute an exact distribution of likelihood ratios that can be applied to any LR-based model. The distribution may have several applications, but is used here to compute a p-value that corresponds to the observed likelihood ratio. The p-value is the probability that a profile under the defense hypothesis, substituted for a questioned contributor e.g. suspect, would attain a likelihood ratio which is at least the same magnitude as that observed. The p-value can be thought of as a scaled version of the likelihood ratio, giving a quantitative measure of the strength of the evidence relative to the specified hypotheses and the model used for the analysis. The algorithm is demonstrated on examples based on real data. R code for the algorithm is freely available in the R package euroMix.

Keywords: Complex mixtures; Distribution of likelihood ratios; Likelihood ratios; p-Values.