Evaluation of glass evidence at activity level: A new distribution for the background population

For evidence evaluation of the physicochemical properties of glass at activity level a well-known formula introduced by Evett & Buckleton [1,2] is commonly used. Parameters in this formula are, amongst others, the probability in a background population to find on somebody's clothing the observed number of glass sources and the probability in a background population to find on somebody's clothing a group of fragments with the same size as the observed matching group. Recently, for efficiency reasons, the Netherlands Forensic Institute changed its methodology to measure not all the glass fragments but a subset of glass fragments found on clothing. Due to the measurement of subsets, it is difficult to get accurate estimates for these parameters in this formula. We offer a solution to this problem. The heart of the solution consists of relaxing the assumption of conditional independence of group sizes of background fragments, and modelling the probability of an allocation of background fragments into groups given a total number of background fragments by a two-parameter Chinese restaurant process (CRP) [3]. Under the assumption of random sampling of fragments to be measured from recovered fragments in the laboratory, parameter values for the Chinese restaurant process may be estimated from a relatively small dataset of glass in other relevant cases. We demonstrate this for a dataset of glass fragments collected from upper garments in casework, show model fit and provide a prototypical calculation of an LR at activity level accompanied with a parameter sensitivity analysis for reasonable ranges of the CRP parameter values. Considering that other laboratories may want to measure subsets as well, we believe this is an important alternative approach to the evaluation of numerical LRs for glass analyses at activity level.