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Auxiliary variable methods such as the Parallel Tempering and the clusterMonte Carlo methods generate samples that follow a target distribution by usingproposal and auxiliary distributions. In sampling from complex distributions,these algorithms are highly more efficient than the standard Markov chain MonteCarlo methods. However, their performance strongly depends on their parametersand determining the parameters is critical. In this paper, we proposed analgorithm for adapting the parameters during drawing samples and proved theconvergence theorem of the adaptive algorithm. We applied our algorithm to theParallel Tempering. That is, we developed adaptive Parallel Tempering thattunes the parameters on the fly. We confirmed the effectiveness of ouralgorithm through the validation of the adaptive Parallel Tempering, comparingsamples from the target distribution by the adaptive Parallel Tempering andsamples by conventional algorithms.

Adaptive Markov Chain Monte Carlo for Auxiliary Variable Method and Its Application to Parallel Tempering