Following the Daubert ruling in 1993, forensic evidence based on fingerprints was first challenged in the 1999 case of the U.S. versus Byron C. Mitchell and, subsequently, in 20 other cases involving fingerprint evidence. The main concern with the admissibility of fingerprint evidence is the problem of individualization, namely, that the fundamental premise for asserting the uniqueness of fingerprints has not been objectively tested and matching error rates are unknown. In order to assess the error rates, we require quantifying the variability of fingerprint features, namely, minutiae in the target population. A family of finite mixture models has been developed in this paper to represent the distribution of minutiae in fingerprint images, including minutiae clustering tendencies and dependencies in different regions of the fingerprint image domain. A mathematical model that computes the probability of a random correspondence (PRC) is derived based on the mixture models. A PRC of 2.25$\,\times 10^{-6}$corresponding to 12 minutiae matches was computed for the NIST4 Special Database, when the numbers of query and template minutiae both equal 46. This is also the estimate of the PRC for a target population with a similar composition as that of NIST4.

Authentication systems based on biometric features (e.g., fingerprint impressions, iris scans, human face images, etc.) are increasingly gaining widespread use and popularity. Often, vendors and owners of these commercial biometric systems claim impressive performance that is estimated based on some proprietary data. In such situations, there is a need to independently validate the claimed performance levels. System performance is typically evaluated by collecting biometric templates from n different subjects, and for convenience, acquiring multiple instances of the biometric for each of the n subjects. Very little work has been done in 1) constructing confidence regions based on the ROC curve for validating the claimed performance levels and 2) determining the required number of biometric samples needed to establish confidence regions of prespecified width for the ROC curve. To simplify the analysis that address these two problems, several previous studies have assumed that multiple acquisitions of the biometric entity are statistically independent. This assumption is too restrictive and is generally not valid. We have developed a validation technique based on multivariate copula models for correlated biometric acquisitions. Based on the same model, we also determine the minimum number of samples required to achieve confidence bands of desired width for the ROC curve. We illustrate the estimation of the confidence bands as well as the required number of biometric samples using a fingerprint matching system that is applied on samples collected from a small population.