Bayesian Statistics and MCMC Methods

This chapter gives a short introduction to the Bayesian paradigm for inference and an overview of the Markov chain Monte Carlo (henceforth MCMC) algorithms used in the rest of the book. For a more thorough discussion on Bayesian statistics, the reader is referred to Koop [2003], for instance. Further details on MCMC methods can be found in Chib and Greenberg [1996], Smith and Roberts [1993], Tierney [1994]. The reader who is familiar with these topics can skip this part of the book and go to the first chapter dedicated to the Bayesian estimation of GARCH models, on page 17.

The plan of this chapter is as follows. The Bayesian paradigm is introduced in Sect. 2.1. MCMC techniques are presented in Sect. 2.2 where we introduce the Gibbs sampler as well as the Metropolis-Hastings algorithm. We also briey discuss some practical implementation issues.