Exact sampling, specifically coupling from the past (CFTP), allows users to sample exactly from the stationary distribution of a Markov chain. During its nearly 20 years of existence, exact sampling has evolved into perfect simulation, which enables high-dimensional simulation from interacting distributions.
Perfect Simulation illustrates the application of perfect simulation ideas and algorithms to a wide range of problems. The book is one of the first to bring together research on simulation from statistics, physics, finance, computer science, and other areas into a unified framework. You will discover the mechanisms behind creating perfect simulation algorithms for solving an array of problems.
The author describes numerous protocol methodologies for designing algorithms for specific problems. He first examines the commonly used acceptance/rejection (AR) protocol for creating perfect simulation algorithms. He then covers other major protocols, including CFTP; the Fill, Machida, Murdoch, and Rosenthal (FMMR) method; the randomness recycler; retrospective sampling; and partially recursive AR, along with multiple variants of these protocols. The book also shows how perfect simulation methods have been successfully applied to a variety of problems, such as Markov random fields, permutations, stochastic differential equations, spatial point processes, Bayesian posteriors, combinatorial objects, and Markov processes.
Table of Contents:
Introduction. Acceptance/Rejection. Coupling from the Past. Bounding Chains. Advanced Techniques Using Coalescence. Coalescence on Continuous and Unbounded State Spaces. Spatial Point Processes. The Randomness Recycler. Advanced Acceptance/Rejection. Stochastic Differential Equations. Applications and Limitations of Perfect Simulation.
About the Author :
Mark L. Huber is the Fletcher Jones Associate Professor of Mathematics and Statistics and George R. Roberts Fellow at Claremont McKenna College. Dr. Huber works in the area of computational probability, designing Monte Carlo methods for applications in statistics and computer science. His research interests include applied mathematics, calculus, computers, probability, and statistics. He earned a PhD from Cornell University.
Review :
"... The author himself was at the center of this ..., being the author of a number of important articles on perfect simulation. This places him ideally to write the first book fully dedicated to the development of the field. Moreover, he is known as a speaker who has the ability to convey complex mathematical ideas in a clear manner. The writing here follows suit; I found it crisp and concise. ... The book has no conventional exercises. Going through its theoretical derivations, however, can be a useful, yet nontrivial exercise. The notions are clearly defined and illustrated by examples that start simple and grow more complex as the readers' understanding grows." -Radu V. Craiu, University of Toronto, in Journal of the American Statistical Association, January 2017 "This book offers the first comprehensive description of many fascinating perfect simulation techniques, which mainly have emerged within the last twenty years. It is enjoyable reading." -Jesper Moller, Professor of Statistics, Department of Mathematical Science, Aalborg University "... a close to perfect entry to a decade of work on perfect sampling. If you have not heard of the concept before, consider yourself lucky to be offered such gentle guidance into it. If you have dabbled with perfect sampling before, reading the book will be like meeting old friends and hearing about their latest deeds: Mark Huber's book should bring you a new perspective on the topic." -Christian Robert, Universite Paris Dauphine and University of Warwick
