The Bayes solution to the unsupervised sequential learning problem induced by a mixture model for the two-class signal versus noise decision problem generates a computational and storage explosion. A quasi-Bayes approximate learning procedure is proposed that avoids the computational explosion while retaining the flavor of the Bayes solution. Convergence is established and efficiency is investigated.

The choice of a gain function in recursive estimation of prior probabilities using a mixture is discussed. In particular, the rate of convergence of two existing schemes is shown to be related to their respective gain functions. Numerical comparisons are made and an improved scheme is proposed.

Unsupervised Bayes sequential learning procedures for classification and estimation are often useless in practice because of the amount of computation required. In this paper, a version of a two-class decision problem is considered, and a quasi-Bayes procedure is motivated and defined. The proposed procedure mimics closely the formal Bayes solution while involving only a minimal amount of computation. Convergence properties are established and some numerical illustrations provided. The approach compares favorably with other non-Bayesian learning procedures that have been proposed and can be extended to more general situations.