by Duncan Murdoch (University of Western Ontario, Canada) and Xiao-Li Meng (University of Chicago, USA)
Perfect sampling using the coupling from the past (CFTP) algorithm was introduced by
Propp and Wilson in 1996. In much the way rejection sampling allows one to convert
samplers from one distribution into samplers from another, CFTP allows one to convert
Markov chain Monte Carlo algorithms from approximate samplers of the steady-state
distribution into perfect ones. Since 1996 CFTP has been applied to many different Markov
chains. However, its use in routine Bayesian computation is still in the early stages of
development. This paper provides a couple of building blocks for its potentially routine
application in Bayesian mixture priors, including a t mixture coupler, and
demonstrates the types of difficulties that currently prevent CFTP from being applied
routinely in Bayesian computation.
Keywords: Coupling from the past, Exact sampling, MCMC, Mixtures
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