Generalized fiducial factor: an alternative to the Bayes factor for forensic identification of source problems

One formulation of forensic identification of source problems is to determine the source of trace evidence, for instance, glass fragments found on a suspect for a crime. The current state of the science is to compute a Bayes factor (BF) comparing the marginal distribution of measurements of trace evidence under two competing propositions for whether or not the unknown source evidence originated from a specific source. The obvious problem with such an approach is the ability to tailor the prior distributions (placed on the features/parameters of the statistical model for the measurements of trace evidence) in favor of the defense or prosecution, which is further complicated by the fact that the typical number of measurements of trace evidence is typically sufficiently small that prior choice/specification has a strong influence on the value of the BF. To remedy this problem of prior specification and choice, we develop an alternative to the BF, within the framework of generalized fiducial inference (GFI), that we term a {\em generalized fiducial factor} (GFF). Furthermore, we demonstrate empirically, on the synthetic and real Netherlands Forensic Institute (NFI) casework data, deficiencies in the BF and classical/frequentist likelihood ratio (LR) approaches.