Deconvolution of dust mixtures by latent Dirichlet allocation in forensic science

Dust particles recovered from the soles of shoes may be indicative of the sites recently visited by an individual, and, in particular, of the presence of an individual at a particular site of interest, e.g., the scene of a crime. By describing the dust profile of a given site by a multinomial distribution over a fixed number of dust particle types, we can define the probability distribution of the mixture of dust recovered from the sole of a shoe via Latent Dirichlet Allocation. We use Variational Bayesian Inference to study the parameters of the model, and use their resulting posterior distributions to make inference on (a) the contributions of sites of interest to a dust mixture, and (b) the particle profiles associated with these sites.