Deconvolution of dust mixtures

Abstract While most evidence types considered by forensic scientists result from the interactions between criminals, objects or victims at crime scenes, dust evidence arises from the mere presence of individuals and objects at locations of interest. Dust is ubiquitous. Yet, the use of dust evidence is anecdotical and is limited to cases where rare and characteristic particles are observed. The dust at any given location contains a large number of particles from different types and the dust present on an object or individual traveling across locations may be indicative of the locations 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. In this paper, we propose to represent dust mixtures as vectors of counts of the individual particles, which can be characterised by any appropriate analytical technique. This strategy enables us to describe a dust mixture as a mixture of multinomial distributions over a fixed number of dust particle types. Using a Latent Dirichlet Allocation model, we make inference on (a) the contributions of sites of interest to a dust mixture, and (b) the particle profiles associated with these sites.