Wen, Zhijian

Bayesian modelling for glass refractive index

Wen Zhijian¹, James Curran¹, Sallyann Harbison², and Douglas Elliot²

1. Department of Statistics, The University of Auckland

2. Institute of Environmental Science and Research Ltd, Auckland

Glass is a common type of evidence in forensic science. Broken glass recovered from a particular suspect may have simliar physical common characteristics with 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 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 the characteristics of the glass - essentially the probability distribution used to model the physical characteristics of recovered glass. Typical characteristics used in case work are the chemical profile of glass and the refractive index measurement. There is a considerable body of scientific literature devoted to the modelling of this information. Aitken and Lucy (2004) described a multivariate kernel density estimation to analyse the chemical profile of glass. Lucy and Zadora (2011) used kernel density estimation to model the change of the refractive index before and after annealing procedures. Our aim is to construct a Bayesian semi-parametric model, the Dirichlet Process Mixture Model, to model the glass refractive index measurement. The results of the analysis can be used to compute the density of such quantity given certain refractive index and extra information on the source glass.

NZSAStudent This presentation is eligible for the NZSA Student Prize.

References

Aitken, Colin GG, and David Lucy. 2004. “Evaluation of Trace Evidence in the Form of Multivariate Data.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 53 (1). Wiley Online Library:109–22.

Lucy, David, and Grzegorz Zadora. 2011. “Mixed Effects Modelling for Glass Category Estimation from Glass Refractive Indices.” Forensic Science International 212 (1-3). Elsevier:189–97.