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

Deconvolution of dust mixtures by latent Dirichlet allocation in forensic science