Catalytic perfect simulation
type: Item
instance of: scholarly article
title: Catalytic perfect simulation
zbMATH Open document ID: 0999.60069
DOI: 10.1023/A:1012205210377
published in: Methodology and Computing in Applied Probability
publication date: 2002-08-20T00:00:00Z
review text: The aim of the present paper is to introduce a general methodology for perfect simulation technique. The paper describes how to convert an existing Markov chain implementation with prescribed stationary distribution, so that perfect samples from the target density to be read off the sample path (at random time intervals). Three important approaches are competing to accomplish this perfect sampling methodology within a general Markov chain: (1) The Read-Once CFTP (Coupling From The Past) algorithm of \textit{D. B. Wilson} [Random Struct. Algorithms 16, No. 1, 85-113 (2000; Zbl 0952.60072)] (2) The second approach used is due to D. Murdoch (1999), and is aimed to obtain a uniformly ergodic Markov chain by utilizing iterations from a merely positive recurrent chain. This is done by inserting regularly a step from an independence sampler with a sufficiently heavy tailed proposal distribution (usually the prior in a Bayesian posterior simulation problem). The independence sampler is one of the simplest types of Metropolis-Hastings algorithms, where the sequence of proposed transitions is merely made up of an independent, identically distributed sequence of random variables. (3) The third involved method belongs to the authors, and provides a coupling construction which allows a computationally straightforward approach to the implementation of Wilson's Read-Once CFTP blueprint. The proposed methodology for the perfect simulation is illustrated on two examples of Bayesian posterior distributions: a hierarchical model example, and a finite mixture example.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 65C40
zbMATH DE Number: 1784509
zbMATH Keywords: Markov chains
zbMATH Keywords: perfect simulation techniques
zbMATH Keywords: coupling constructions
zbMATH Keywords: perfect sampling methodology
zbMATH Keywords: Metropolis-Hastings algorithm
zbMATH Keywords: Read-Once CFTP algorithm
author: Laird Breyer
author: Gareth O. Roberts
MaRDI profile type: Publication
full work available at URL: a:1012205210377
OpenAlex ID: W2046379078
description: scientific article; zbMATH DE number 1784509