BAYESIAN MIXTURE MODELS FOR DENSITY ESTIMATION

Mixture models provide a convenient and flexible class of models for density estimation. They are typically used to model data generated from one of a number of different groups. This thesis studies two types of mixture models for density estimation from a Bayesian perspective. First, the Dirichlet process mixture (DPM) model is reviewed as it allows flexible nonparametric modeling. Second, the Markov chain Monte Carlo, Monte Carlo (MC3) method is proposed. The idea behind the MC3 method is to approximate an unknown density with a discrete distribution that has a finite number of support points. From a modeling perspective, MC3 represents a finite mixture model where the mixture components are equally weighted. An efficient slice sampling algorithm is provided to implement the MC3 method. Simulation results show that these two methods produce comparable predictive densities. Differences between the DPM and MC3 from modeling and computation aspects are discussed. We conclude with a discussion of applying the MC3 approach to inference for integral equations, which include the state-price density estimation in finance as a specific example.