The Use of Correlated Binomial Distribution in Estimating Error Rates for Firearm Evidence Identification

In the branch of forensic science known as firearm evidence identification, estimating error rates is a fundamental challenge. Recently, a new quantitative approach known as the congruent matching cells (CMC) method was developed to improve the accuracy of ballistic identifications and provide a basis for estimating error rates. To estimate error rates, the key is to find an appropriate probability distribution for the relative frequency distribution of observed CMCs overlaid on a relevant measured firearm surface such as the breech face of a cartridge case. Several probability models based on the assumption of independence between cell pair comparisons have been proposed, but the assumption of independence among the cell pair comparisons from the CMC method may not be valid. This article proposes statistical models based on dependent Bernoulli trials, along with corresponding methodology for parameter estimation. To demonstrate the potential improvement from the use of the dependent Bernoulli trial model, the methodology is applied to an actual data set of fired cartridge cases.