Perfect Simulation

Mark L. Huber

November 19, 2015 by Chapman and Hall/CRC
Reference - 228 Pages - 18 B/W Illustrations
ISBN 9781482232448 - CAT# K22899
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

USD$89.95

Add to Wish List
FREE Standard Shipping!

Features

  • Explains the building blocks of perfect simulation algorithms
  • Provides detailed descriptions and examples of how sampling works
  • Describes the two most important protocols for creating perfect simulation algorithms: AR and CFTP
  • Presents algorithms for each application discussed
  • Reviews the necessary concepts from measure theory and probability
  • Covers a variety of Markov chains, including Gibbs, Metropolis–Hastings, auxiliary random variables, and the shift move

Summary

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.