Avoiding overstating the strength of forensic evidence: Shrunk likelihood ratios/Bayes factors

Abstract

When strength of forensic evidence is quantified using sample data and statistical models, a concern may be raised as to whether the output of a model overestimates the strength of evidence. This is particularly the case when the amount of sample data is small, and hence sampling variability is high. This concern is related to concern about precision. This paper describes, explores, and tests three procedures which shrink the value of the likelihood ratio or Bayes factor toward the neutral value of one. The procedures are: (1) a Bayesian procedure with uninformative priors, (2) use of empirical lower and upper bounds (ELUB), and (3) a novel form of regularized logistic regression. As a benchmark, they are compared with linear discriminant analysis, and in some instances with non-regularized logistic regression. The behaviours of the procedures are explored using Monte Carlo simulated data, and tested on real data from comparisons of voice recordings, face images, and glass fragments.