Bayesian analysis of finite Gaussian mixtures

The problem considered in this paper is parameter estimation of a multivariate Gaussian mixture distribution with a known number of components. The paper presents a new Bayesian method which sequentially processes the observed data points by forming candidate sequences of labels assigning data points to mixture components. Using conjugate priors, we derive analytically a recursive formula for the computation of the probability of each label sequence. The practical implementation of this algorithm keeps only a predefined number of the highest ranked label sequences with the ranking based on posterior probabilities. We show by numerical simulations that the proposed technique consistently outperforms both the k-means and the EM algorithm.