Bayesian estimation of dynamic mixture models by wavelets

Abstract

Gaussian mixture models are used successfully in various statistical learning applications. The good results provided by these models encourage several generalizations of them. Among possible adaptations, one can assume a dynamic behavior for the mixture weights to make the model more adaptive to different data sets. When estimating this dynamic behavior, wavelet bases have emerged as an alternative. However, in the existing literature, the wavelet-based methods only estimate the dynamic mixing probabilities, failing to provide estimates for the component parameters of the mixture model. In this work, we propose two approaches based on orthonormal wavelets to estimate the dynamic mixture weights under efficient MCMC algorithms that allows us to estimate the component parameters from their posterior samples. We use simulated and real data sets to illustrate both approaches' performances. The results indicate that the proposed methods are promising and computationally efficient alternatives for estimating jointly the dynamic weights and the component parameter of two Gaussian mixtures.