Markov Chain Monte Carlo Method and Perfect Simulation

Abstract

Markov Chain Monte Carlo method is used to sample from complicated multivariate distribution with normalizing constants that may not be computable and from which direct sampling is not feasible. Recent years have seen the development of a new, exciting generation of Markov Chain Monte Carlo method: perfect simulation algorithms. In this thesis, we give a review of the new perfect simulation algorithms using Markov chains, focussed on the method called Coupling From The Past, since it allows not only an approximate but perfect (exact) simulation of the stationary distribution of finite state space Markov chain.