Nonparametric Bayesian methods: a gentle introduction and overview
Steven N. MacEachern · Communications for Statistical Applications and Methods · 2016
Nonparametric Bayesian methods have seen rapid and sustained growth over the past 25 years.We present a gentle introduction to the methods, motivating the methods through the twin perspectives of consistency and false consistency.We then step through the various constructions of the Dirichlet process, outline a number of the basic properties of this process and move on to the mixture of Dirichlet processes model, including a quick discussion of the computational methods used to fit the model.We touch on the main philosophies for nonparametric Bayesian data analysis and then reanalyze a famous data set.The reanalysis illustrates the concept of admissibility through a novel perturbation of the problem and data, showing the benefit of shrinkage estimation and the much greater benefit of nonparametric Bayesian modelling.We conclude with a too-brief survey of fancier nonparametric Bayesian methods.