Sampling variability in forensic likelihood-ratio computation: A simulation study

Recently, in the forensic biometric community, there is a growing interest to compute a metric called “likelihood- ratio‿ when a pair of biometric specimens is compared using a biometric recognition system. Generally, a biomet- ric recognition system outputs a score and therefore a likelihood-ratio computation method is used to convert the score to a likelihood-ratio. The likelihood-ratio is the probability of the score given the hypothesis of the prose- cution, Hp (the two biometric specimens arose from a same source), divided by the probability of the score given the hypothesis of the defense, Hd (the two biometric specimens arose from different sources). Given a set of training scores under Hp and a set of training scores under Hd, several methods exist to convert a score to a likelihood-ratio. In this work, we focus on the issue of sampling variability in the training sets and carry out a detailed empirical study to quantify its effect on commonly proposed likelihood-ratio computation methods. We study the effect of the sampling variability varying: 1) the shapes of the probability density func- tions which model the distributions of scores in the two training sets; 2) the sizes of the training sets and 3) the score for which a likelihood-ratio is computed. For this purpose, we introduce a simulation framework which can be used to study several properties of a likelihood-ratio computation method and to quantify the effect of sampling variability in the likelihood-ratio computation. It is empirically shown that the sampling variability can be considerable, particularly when the training sets are small. Furthermore, a given method of likelihood- ratio computation can behave very differently for different shapes of the probability density functions of the scores in the training sets and different scores for which likelihood-ratios are computed.