Density-based matching rule: Optimality, estimation, and application in forensic problems

We consider matching problems where the goal is to determine whether two observations randomly drawn from a population with multiple (sub)groups are from the same (sub)group. This is a key question in forensic science, where items with unidentified origins from suspects and crime scenes are compared to objects from a known set of sources to see if they originated from the same source. We derive the optimal matching rule under known density functions of data that minimizes the decision error probabilities. Empirically, the proposed matching rule is computed by plugging parametrically estimated density functions using training data into the formula of the optimal matching rule. The connections between the optimal matching rule and existing methods in forensic science are explained. In particular, we contrast the optimal matching rule to classification and also compare it to a score-based approach that relies on similarity features extracted from paired items. Numerical simulations are conducted to evaluate the proposed method and show that it outperforms the existing methods in terms of a higher ROC curve and higher power to identify matched pairs of items. We also demonstrate the utility of the proposed method by applying it to a real forensic data analysis of glass fragments.