Gibbs Sampling, Conjugate Priors and Coupling

摘要

We give a large family of simple examples where a sharp analysis of the Gibbs sampler can be proved by coupling. These examples involve standard statistical models - exponential families with conjugate priors or location families with natural priors. Our main approach uses a single eigenfunction (always explicitly available in the examples in question) and stochastic monotonic-ity. We give a satisfactory treatment of several examples that have defeated previous attempts at analysis.