Bayesian Density Estimation and Inference Using Mixtures

TLDR

Mixture models, such as Dirichlet process mixtures, are widely used for density estimation, with normal mixtures as a common special case. The study presents Bayesian inference methods for density estimation using Dirichlet process mixture models. The authors employ efficient simulation techniques to approximate prior, posterior, and predictive distributions in these mixture models. The methods enable direct inference on smoothing, uncertainty, modality, component counts, and provide convergence guarantees for general normal mixture models.

Abstract

Abstract We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior, and predictive distributions. This allows for direct inference on a variety of practical issues, including problems of local versus global smoothing, uncertainty about density estimates, assessment of modality, and the inference on the numbers of components. Also, convergence results are established for a general class of normal mixture models.