A Bayesian approach to mixture models and transdimensional Markov chains

Abstract

A general Bayesian sampling method is developed that uses parallel chains to select between models and to average the predictive density over such models. The method applies to both non-nested models and to nested models, and is particularly useful for mixtures of complex component models, where a novel approach to overcome the label-switching problem is used. The method is illustrated with real and simulated data in model-averaging over alternative financial time series models, mixtures of normal distributions, and mixtures of smoothing spline models. In chapter 4 the method is extended to improve the efficiency of the sampling scheme. Mixture models are revisited in chapter 5 and compared to model averaging on simulated data sets and financial time series data. Chapter 6 applies mixture models to account for non-stationarity in time series data.