A composite Bayesian hierarchical model of compositional data with zeros

We present an effective approach for modelling compositional data with large concentrations of zeros and several levels of variation, applied to a database of elemental compositions of forensic glass of various use types. The procedure consists of the following: (i) partitioning the data set in subsets characterised by the same pattern of presence/absence of chemical elements and (ii) fitting a Bayesian hierarchical model to the transformed compositions in each data subset. We derive expressions for the posterior predictive probability that newly observed fragments of glass are of a certain use type and for computing the evidential value of glass fragments relating to two competing propositions about their source. The model is assessed using cross-validation, and it performs well in both the classification and evidence evaluation tasks.