Adaptive Gibbs samplers and related MCMC methods

We consider various versions of adaptive Gibbs and Metropolis- within-Gibbs samplers, which update their selection probabilities (and per- haps also their proposal distributions) on the y during a run, by learning as they go in an attempt to optimise the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions. AMS 2000 subject classications: Primary 60J05, 65C05; secondary 62F15.

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