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Efficient MCMC Schemes for Computationally Expensive Posterior Distributions

Summary: [This abstract is based on the authors' abstract.] This article examines Markov chain Monte Carlo schemes designed to minimize the number of times the posterior distribution must be made when using Bayesian inference if the posterior distribution is computationally expensive. Previously the literature has described a hybrid Monte Carlo-Gaussian process approximation method, which is here expanded in three ways. First, the original method is combined with tempering schemes to deal with multimodal distributions. Second, the original posterior distribution is replaced with the Gaussian approximation. Finally, the Gaussian approximation is used for high temperature chains while the original target posterior distribution is used for the lowest temperature chain. An example is presented of a rainfall-runoff model with a multimodal posterior distribution.

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  • Topics: Statistics
  • Keywords: Approximation, Bayesian methods, Distributions, Markov chains, Monte Carlo methods, Computer models, Gaussian processes, Parallel tempering
  • Author: Fielding, Mark; Nott, David J.; Liong, Shie-Yui
  • Journal: Technometrics