Bayesian mixture modelling for glass refractive index measurement

Abstract

Glass is a common type of physical evidence in forensic science. Broken glass recovered from a suspect may have similar physical characteristics to glass collected at a crime scene and therefore can be used as evidence. Statistical treatment of this evidence involves computing a measure of the weight of evidence. This may be done in a Bayesian framework that incorporates information from the circumstances of the crime. One of the most crucial quantities in this calculation is the assessment of the relative rarity of the characteristics of the glass, essentially the probability distribution used to model the physical characteristics of recovered glass. Typical characteristics used in casework are the elemental composition of glass and the refractive index measurement. There is a considerable body of scientific literature devoted to the modelling of this information. For example a kernel density estimation has been used to model the background population of glass based on the refractive index measurement and a multivariate Gaussian finite mixture model has been used to model the elemental composition of glass. In this paper, we present an alternative approach, the Dirichlet Process Mixture Model, to model the glass refractive index measurement in a Bayesian methodology. A key advantage is that using this method allows us to model the probability density distribution of refractive index measurements in a more flexible way.