Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

18Nonparametric Bayes

Bayesian (bey' ‐zhn) . 1. Result of breeding a statistician with a clergyman to produce the much sought honest statistician.

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This chapter is about nonparametric Bayesian inference. Understanding the computational machinery needed for non‐conjugate Bayesian analysis in this chapter can be quite challenging, and it is beyond the scope of this text. Instead, we will use specialized software, WinBUGS, to implement complex Bayesian models in a user‐friendly manner. Some applications of WinBUGS have been discussed in Chapter 4, and an overview of WinBUGS is given in the Appendix B.

Our purpose is to explore the useful applications of the nonparametric side of Bayesian inference. At first glance, the term nonparametric Bayes might seem like an oxymoron; after all, Bayesian analysis is all about introducing prior distributions on parameters. Actually, nonparametric Bayes is often seen as a synonym for Bayesian models with process priors on the spaces of densities and functions. Dirichlet process (DP) priors are the most popular choice. However, many other Bayesian methods are nonparametric in spirit. In addition to DP priors, Bayesian formulations of contingency tables and Bayesian models on the coefficients in atomic decompositions of functions will be ...