Markov Chain Monte Carlo Methods: Part I: Simple Monte Carlo
Mohan Delampady · 2002
In earlier articles in Resonance mentioned in the References below, various authors discussed Monte Carlo simulation methods and their applications. In the two articles by Chakraborty (2002a, 2002b), Markov Chain Monte Carlo (MCMC) was introduced with examples and its method of simulation explained. In this series of articles we describe MCMC methods in general and their rationale, discuss special cases of the MCMC algorithms and work out examples and applications in Statistics, especially Bayesian Statistics. In Part I, we discuss the independent identically distributed (IID) Monte Carlo procedure (i.e., without a real Markov chain structure) with applications to integration including integration in a Bayesian context. In Part II, we describe the algorithms of MCMC and explain how they work. In Part III, we discuss some Statistical Preliminaries which are required to understand Statistical Applications of MCMC described in Part IV. The most significant applications of MCMC are in Bayesian Inference, an