A Quasi-Bayes Sequential Procedure for Mixtures

Abstract

Coherent Bayes sequential learning and classification procedures are often useless in practice because of ever-increasing computational requirements. On the other hand, computationally feasible procedures may not resemble the coherent solution, nor guarantee consistent learning and classification. In this paper, a particular form of classification problem is considered and a "quasi-Bayes" approximate solution requiring minimal computation is motivated and defined. Convergence properties are established and a numerical illustration provided.

Almost sure convergence of Titterington's recursive estimator for mixture models

“…To overcome this difficulty, on-line quasi-Bayes learning (cf. Huo and Lee, 1997;Smith and Makov, 1978) first approximates the successive posterior distributions by the ''closest'' tractable distribution within a given class P, under the criterion that both distributions have the same mode, and the EM algorithm is next applied to estimate the hyperparameters f of the approximate posterior distribution and model parameters l are incrementally updated. Empirical evidence showed that the quasi-Bayes algorithm in general converges to a good solution and it has a similar behavior with the batch MAP algorithm (cf.…”

Modeling Lake-Chemistry Distributions: Approximate Bayesian Methods for Estimating a Finite-Mixture Model

“…Most of the techniques work with the sequential form of calculating and simplifying the MODELING LAKE-CHEMISTRY DISTRIBUTIONS 443 posterior (e.g., Bernard0 and Giron 1986;Smith and Makov 1978). By simplifying the posterior after each observation, these methods avoid many computational problems associated with an exact analysis.…”

Probabilistic Networks and Expert Systems

“…. . Techniques include the 'probabilistic teacher', in which the missing variables are randomly fixed according to their current posterior distribution, and 'quasi-Bayes' (Smith and Makov 1978) or 'fractional updating' (Titterington 1976). Techniques include the 'probabilistic teacher', in which the missing variables are randomly fixed according to their current posterior distribution, and 'quasi-Bayes' (Smith and Makov 1978) or 'fractional updating' (Titterington 1976).…”