Abstract
In this paper we present extensions to the original adaptive Parallel Tempering algorithm. Two different approaches are presented. In the first one we introduce state-dependent strategies using current information to perform a swap step. It encompasses a wide family of potential moves including the standard one and Equi-Energy type move, without any loss in tractability. In the second one, we introduce online trimming of the number of temperatures. Numerical experiments demonstrate the effectiveness of the proposed method.
Highlights
Markov chain Monte Carlo (MCMC) is a generic method to approximate an integral of the formI := f (y)π(y)dy, RdElectronic supplementary material The online version of this article contains supplementary material, which is available to authorized users.The random walk Metropolis algorithm (Metropolis et al 1953) often works well, provided the target density π is, roughly speaking, sufficiently close to unimodal
In this article it was demonstrated that the Parallel Tempering algorithm’s efficiency is highly dependent upon the number of initial temperature levels; for underestimating that number leads to poor quality estimates resulting from neglecting some of the modes of the distribution of interest
We have developed an algorithm with adaptable temperature scheme
Summary
Markov chain Monte Carlo (MCMC) is a generic method to approximate an integral of the form. 2011; Roberts and Rosenthal 2012) These theoretical findings were used to derive adaptive version of the Parallel Tempering (Miasojedow et al 2013a). Another approach to temperature tuning can be found in (Behrens et al 2012). The temperature adaptation scheme depends on the parameters of the adaptive random walks applied in the parallelised Metropolis-Hastings stage of the algorithm in case when the state space amounts to be the usual Rd. We have showed that the proposed algorithm satisfies the Law of Large numbers, in the same setting as in Miasojedow et al (2013a).
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