Abstract
The coupling method has been an enormously useful tool for studying the mixing time of Markov chains and as the basis of perfect sampling algorithms such as Coupling From the Past. Several methods such as Wilson's layered multishift coupling and Breyer and Robert' catalytic coupling have been introduced to use the coupling approach on continuous state spaces. This work builds upon these approaches by using a simple coupling for small Metropolis moves together with catalytic coupling. As an application, the analysis of a Markov chain for the autonormal distribution in the Wasserstein metric of A. Gibbs is extended to an analysis in total variation distance. Moreover, a perfect sampling algorithm is constructed that has mean running time O (N ln N) time for fixed values of the parameters of the model.
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