Global Distributional Assumptions for a Local False Discovery Rate-Based Assessment of Forensic and Biometric Matching System Capacity

In forensic science, we are typically focused on making a comparison between two sets of evidence; one associated with a collection of trace objects and one associated with a set of control samples collected from a known source. Forensic individuality refers to the proposition that each individual source in a population of sources has a unique distribution of traces. In biometric verification tasks, we can make comparisons between two biometric samples, one associated with a query object and one associated with the control sample(s) collected from a specified biometric source. Biometric individuality describes the rate at which we encounter biometric samples from two distinct sources that are indistinguishable, with respect to a biometric comparison technique. We test global distribution assumptions by leveraging local false discovery rates and the minimum Cramér -von Mises statistic to obtain the number of observed sources that satisfy the normality assumption. Working with the raw similarity scores between two samples of traces, we assume if a similarity score arises from two indistinguishable sources, then it follows a uniform distribution. If the two comparisons are from distinguishable profiles, we assume the comparison score follows a type of beta distribution. With these two distributions, we use mixture modeling based on minimum Cramér-von Mises statistics and standard likelihood-based estimates to characterize the proportion of comparisons stemming from a uniform distribution; which in turn provides an estimate of the biometric capacity of the system. We illustrate these ideas with a data set of smokeless powder samples for small arms propellants.