In this paper, we study the general verification problem from a Bayesian viewpoint. In the Bayesian approach, the verification decision is made by evaluating Bayes factors against a critical threshold. The calculation of the Bayes factors in turn requires the computation of several Bayesian predictive densities. As a case study, we apply the method to speaker verification based on the Gaussian mixture model (GMM). We propose an efficient algorithm to calculate the Bayes factors for the GMM, where the Viterbi approximation is adopted in the computation of joint Bayesian predictive densities. We evaluate the proposed method for the NIST98 speaker verification evaluation data. Experimental results show that new Bayesian approach achieves moderate improvements over a well-trained baseline system using the conventional likelihood ratio test.