As biometric authentication systems become more prevalent, it is becoming increasingly important to evaluate their performance. This paper introduces a novel statistical method of performance evaluation for these systems. Given a database of authentication results from an existing system, the method uses a hierarchical random effects model, along with Bayesian inference techniques yielding posterior predictive distributions, to predict performance in terms of error rates using various explanatory variables. By incorporating explanatory variables as well as random effects, the method allows for prediction of error rates when the authentication system is applied to potentially larger and/or different groups of subjects than those originally documented in the database. We also extend the model to allow for prediction of the probability of a false alarm on a "watch-list” as a function of the list size. We consider application of our methodology to three different face authentication systems: a filter-based system, a Gaussian Mixture Model (GMM)-based system, and a system based on frequency domain representation of facial asymmetry.