Graphical Models in Applied Multivariate Statistics
Graphical Models in Applied Multivariate Statistics
Factored principal components analysis, with applications to face recognition
Statistics and Computing
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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. There are commonly three levels of variation in such evidence. First, there is measurement error on the individual items. Then, individual items are gathered in groups and there is variation within and between groups. There are also commonly many variables which can be measured on the items, such as elemental or chemical composition. There are usually inadequate data to enable proper estimation of a full parametric model to be made. A method is described here for evaluating the evidence by means of a likelihood ratio. The likelihood ratio compares the probability of the measurements on the evidence assuming a common source for evidence from the crime scene and evidence associated with the suspect with the probability of the measurements on the evidence assuming different sources for the crime scene and suspect evidence. It is a well-documented measure of the value of the evidence. A three-level model for multivariate normal data is described. The structure of the data is determined through consideration of the inverse of the covariance matrix from which a graphical model may be determined. This enables a considerable reduction in the parameterisation from the full model whilst retaining a credible dependence structure, not recognised in a model which assumes full independence. The model for the structure of the data thus obtained provides a novel solution to a problem in forensic science where full independence is often assumed for multivariate data. The performances of the derived models are investigated on a data set provided by a European forensic science laboratory.