Bayesian computational methods

TL;DR

This paper discusses key computational challenges in Bayesian statistics, such as mixture estimation and model choice, and reviews related computational solutions, serving as an introductory overview of Bayesian computational methods.

Contribution

It provides a concise overview of common computational problems in Bayesian statistics and links them with existing computational solutions, focusing on mixture estimation and model choice.

Findings

Identifies major computational challenges in Bayesian analysis.

Connects problems with existing computational methods.

Serves as an introductory guide to Bayesian computational techniques.

Abstract

In this chapter, we will first present the most standard computational challenges met in Bayesian Statistics, focussing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions. Of course, this chapter is only a terse introduction to the problems and solutions related to Bayesian computations. For more complete references, see Robert and Casella (2004, 2009), or Marin and Robert (2007), among others. We also restrain from providing an introduction to Bayesian Statistics per se and for comprehensive coverage, address the reader to Robert (2007), (again) among others.