Session Slot: 2:00- 3:50 Sunday
Estimated Audience Size:
Session Title: Exact Simulation
Theme Session: No
Applied Session: No
Session Organizer: Green, Peter University of Bristol
Address: Department of Mathematics, University of Bristol, Bristol, BS8 1TW, UK.
Session Timing: 110 minutes total (Sorry about format):
Session Chair: Liu, Jun Stanford University
1. Perfect and Imperfect Simulation
Tweedie, Richard, Colorado State University
Address: Department of Statistics, Colorado State University, Fort Collins CO 80523, USA
Phone: (970) 491 6786
Fax: (970) 491 7895
Abstract: We describe algorithms for simulating random samples from the invariant measures of stochastically ordered Markov chains on spaces which may be continuous. Both ``vertical'' and ``horizontal'' backwards coupling algorithms are introduced. Convergence properties of these algorithms are described, and methods of bounding the results when there are no maximal or minimal elements are outlined.
2. Exact Sampling for Bayesian Inference: Towards General Purpose Algorithms
Murdoch, Duncan, Queens University, Ontario, Canada
Address: Dept. of Math. and Stats.
Kingston, Ontario, Canada
Phone: 613 545 2395
Fax: 613 545 2964
Green, Peter, University of Bristol, Bristol, U.K.
Abstract: Propp and Wilson (1996) described a protocol, called coupling from the past, for exact sampling from a target distribution using a coupled Markov chain Monte Carlo algorithm. In Murdoch and Green (1997) we described methods which can be used to apply coupling from the past to various MCMC samplers on continuous state spaces; rather than following the monotone sampling device of Propp and Wilson, our approach used methods related to gamma-coupling and rejection sampling to simulate the chain, and direct accounting of sample paths to check whether they had coalesced.
In this presentation we will describe methods for coupling the random walk Metropolis-Hastings algorithm based on a pretty dissection of the area under the graph of a symmetric density function. These methods may be applied almost automatically to a wide class of Bayesian hierarchical models.
3. Exact Simulation of Markov Random Fields Using Coupling from the Past
Haggstrom, Olle, Chalmers University of Technology, Sweden
Address: Dept of Mathematics, Chalmers University of Technology, 412 96 Gothenburg, Sweden
Phone: +46 31 7725311
Fax: +46 31 161973
Nelander, Karin, Chalmers University of Technology
Abstract: We discuss the possibility of using the Propp-Wilson coupling from the past (CFTP) approach to generate exact samples from various types of Markov random fields. The focus is mainly on examples rather than on general theory. One of our main messages is that the CFTP thechnique is applicable far beyond the class of stochastically monotone systems originally considered by Propp and Wilson. The talk is based on joint work with Karin Nelander.
List of speakers who are nonmembers: