The evaluation of evidence in the form of multivariate data and in the absence of population data

Models were investigated for evidence evaluation for multivariate compositional data with zeros and for sample size determination.

There were two key findings



Likelihood ratio models for classification and comparison for compositional data are developed to include consideration of zeros. The proposed model gave very satisfactory results for the glass comparison problem and for most of the classification tasks for glass. Results of comparison of paints were also highly satisfactory, with only 3.0% false positive answers and 2.8% false negative answers.



Procedures were reviewed and recommendations made for the choice of the size of a sample to estimate the characteristics of a population consisting of discrete items which may belong to one and only one of a number of categories with examples drawn from forensic science. A conclusion provides recommendations for sampling procedures in various contexts.