TABLE OF CONTENTS Wilfrid Kendall
Department of Statistics
University of Warwick
Coventry CV4 7AL, UK
E-mail: w.s.kendall@warwick.ac.uk
Perfect simulation refers to the art of converting suitable Markov Chain Monte Carlo algorithms into algorithms which return exact draws from the target distribution, instead of approximations based on long-time convergence to equilibrium. The theoretical concepts underlying perfect simulation have a long history, but they were first drawn together to form a practical simulation technique in the ground-breaking paper of Propp and Wilson [78], which showed how (for example) to obtain exact draws from the critical Ising model on a finite lattice. These lecture notes are organized around four main themes of perfect simulation: the original or classic Coupling From The Past algorithm (CFTP); variations which exploit regeneration ideas such as small-set or split-chain constructions from Markov chain theory (small-set CFTP); generalizations of CFTP which deal with non-monotonic and non-uniformly ergodic examples (dominated CFTP); and finally some theoretical complements.
Perfect simulation refers to the art of converting suitable Markov Chain Monte Carlo (MCMC) algorithms into algorithms which return exact draws from the target distribution, instead of long-time approximations. The theoretical concepts underlying perfect simulation have a long history, but they were first drawn together to form a practical simulation technique in the ground-breaking paper of Propp and Wilson [78], which showed how (for example) to obtain exact draws from the critical Ising model on a finite lattice.
These notes derive from a series of four tutorial lectures given at the...
