A Dirichlet form approach to MCMC optimal scaling

Giacomo Zanella, Mylène Bédard and Wilfrid S. Kendall

Stochastic Processes and their Applications, 2017, vol. 127, issue 12, 4053-4082

Abstract: This paper shows how the theory of Dirichlet forms can be used to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis–Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form methods have the added advantage of providing an explicit construction of the underlying infinite-dimensional context. In particular, this enables us directly to establish weak convergence to the relevant infinite-dimensional distributions.

Keywords: Dirichlet form; Infinite-dimensional stochastic processes; Asymptotic analysis for MCMC; Markov chain Monte Carlo (MCMC); Metropolis–Hastings Random Walk (MHRW) sampler; Mosco convergence; Scaling limits; Optimal scaling; Weak convergence (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:12:p:4053-4082

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DOI: 10.1016/j.spa.2017.03.021

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