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RESEARCH PRODUCT

An Adaptive Parallel Tempering Algorithm

Błażej MiasojedowMatti ViholaEric Moulines

subject

Statistics and ProbabilityScheduleMathematical optimizationta112Adaptive algorithmErgodicityta111Mixing (mathematics)Law of large numbersKernel (statistics)Convergence (routing)Discrete Mathematics and CombinatoricsParallel temperingStatistics Probability and UncertaintyAlgorithmMathematics

description

Parallel tempering is a generic Markov chainMonteCarlo samplingmethod which allows good mixing with multimodal target distributions, where conventionalMetropolis- Hastings algorithms often fail. The mixing properties of the sampler depend strongly on the choice of tuning parameters, such as the temperature schedule and the proposal distribution used for local exploration. We propose an adaptive algorithm with fixed number of temperatures which tunes both the temperature schedule and the parameters of the random-walk Metropolis kernel automatically. We prove the convergence of the adaptation and a strong law of large numbers for the algorithm under general conditions. We also prove as a side result the geometric ergodicity of the parallel tempering algorithm. We illustrate the performance of our method with examples. Our empirical findings indicate that the algorithm can cope well with different kinds of scenarios without prior tuning. Supplementary materials including the proofs and the Matlab implementation are available online. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

10.1080/10618600.2013.778779https://doi.org/10.1080/10618600.2013.778779