Catalytic perfect simulation
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.
scientific article; zbMATH DE number 1784509