Estimation and sample size calculations for correlated binary error rates of biometric identification devices

Biometric Identification Devices (BID’s) compare a physiological measurement of an individual to a database of stored templates. The goal of any BID is to correctly match those two quantities. When the comparison between the measurement and the template is performed the result is either an ”accept” or a ”reject.” For a variety of reasons, errors occur in this process. Consequently, false rejects and false accepts are made. As acknowledged in a variety of papers, e.g. Wayman (1999), Mansfield and Wayman (2002), there is a need for assessing the uncertainty in these error rates for a BID. Despite the binary nature of the outcome from the matching process, it is well known that a binomial model is not appropriate for estimating false reject rates (FRRs) and false accept rates (FARs). This is also implicitly noted by Wayman (1999). Thus, other methods that do not depend on the binomial distribution are needed. Some recent work has made headway on this topic. In Bolle et al. (2000) the authors propose using resampling methods to approximate the cumulative density function. This methodology, the so-called ”subset bootstrap” or ”block bootstrap”, has received some acceptance. Schuckers (2003) has proposed use of the Beta-binomial distribution which is a generalization of the binomial distribution. Like the ”subset bootstrap”, this method assumes conditional independence of the responses for each individual. Utilizing the Beta-binomial, Schuckers outlines a procedure for estimating an error rate when multiple users attempt to match multiple times.