Some Bayesian Nonparametric Models

Publisher Summary This chapter discusses some Bayesian nonparametric models. The aim of this chapter is to describe some popular Bayesian nonparametric models that have been studied extensively, which have found some use in practice as well. The style of the chapter is to highlight the salient features of such models with a view to implementing them. Emphasis is placed on the stochastic process approach to Bayesian nonparametrics, in particular, the Dirichlet process. Moreover, at the present time, the Dirichlet process is to Bayesian nonparametrics what the proportional hazards models is to biostatistics, or more generally, what the normal distribution is to statistics. Finally, Escobar was the first to implement the Dirichlet process using Markov chain Monte Carlo (MCMC) methods, setting the stage for all future applied work in the chaptert. Finally, it should be mentioned that Kuo developed an importance sampler for Dirichlet process models; however, this approach is not as efficient and general as the ideas described in Escobar.