New Perfect Sampling Algorithms with Applications to Bayesian Computations, Engineering, and Finance

• Activity Number: 265
• Type: Contributed
• Date/Time: Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jose Blanchet*+ and Peter W. Glynn and Xiao-Li Meng
• Companies: Harvard University and Stanford University and Harvard University
• Keywords: MCMC ; Perfect-sampling ; regeneration ; fixed-point-equations

Abstract

The path-breaking paper of Propp and Wilson (1996) introduced a simulation protocol called Coupling from the Past (CFTP) that can be used to generate "exact" samples from the stationary distribution of a Markov chain. Other important perfect simulation algorithms have been developed since then (Fill 1998, Kendall 1997, Murdoch and Green 1998, Corcoran and Tweedie 2001). In this paper, we describe two new exact simulation algorithms. The first uses the regenerative structure of positive recurrent Harris chains and is based on Asmussen, Glynn, and Thorisson (1992). We explain how using a bound on a suitably high moment of a regeneration time, one can generate exact samples from the stationary distribution of a positive recurrent Harris chain. The second algorithm is well suited to sample from solutions to stochastic fixed point equations and involves change-of-measure type of ideas. We apply this algorithm to the single-server queue (widely used in engineering) and to stationary ARCH processes (common in financial time series). These algorithms extend recent work of Hobert and Robert (2004) and Ensor and Glynn (2000).