Evaluation of trace evidence in the form of multivariate data

Summary.  The evaluation of measurements on characteristics of trace evidence found at a crime scene and on a suspect is an important part of forensic science. Five methods of assessment for the value of the evidence for multivariate data are described. Two are based on significance tests and three on the evaluation of likelihood ratios. The likelihood ratio which compares the probability of the measurements on the evidence assuming a common source for the crime scene and suspect evidence with the probability of the measurements on the evidence assuming different sources for the crime scene and suspect evidence is a well-documented measure of the value of the evidence. One of the likelihood ratio approaches transforms the data to a univariate projection based on the first principal component. The other two versions of the likelihood ratio for multivariate data account for correlation among the variables and for two levels of variation: that between sources and that within sources. One version assumes that between-source variability is modelled by a multivariate normal distribution; the other version models the variability with a multivariate kernel density estimate. Results are compared from the analysis of measurements on the elemental composition of glass.