Minimising MCMC variance via diffusion limits, with an application to simulated tempering

Abstract

We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth-death chains which themselves satisfy Peskun orderings. We then apply our results to simulated tempering algorithms to establish which choice of inverse temperatures minimises the asymptotic variance of all functionals and thus leads to the most efficient MCMC algorithm.

Published in at http://dx.doi.org/10.1214/12-AAP918 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Optimal scalings for local Metropolis--Hastings chains on nonproduct targets in high dimensions
• Convergence of adaptive and interacting Markov chain Monte Carlo algorithms
• Weak convergence of Metropolis algorithms for non-i.i.d. target distributions

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• Accelerating Parallel Tempering: Quantile Tempering Algorithm (QuanTA)