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Optimal scaling of MCMC beyond Metropolis

Part of: Probabilistic methods, simulation and stochastic differential equations Limit theorems

Published online by Cambridge University Press:  16 December 2022

Sanket Agrawal ,
Dootika Vats Open the ORCID record for Dootika Vats [Opens in a new window] ,
Krzysztof Łatuszyński  and
Gareth O. Roberts
Sanket Agrawal*
Affiliation:
University of Warwick
Dootika Vats*
Affiliation:
Indian Institute of Technology Kanpur
Krzysztof Łatuszyński*
Affiliation:
Indian Institute of Technology Kanpur
Gareth O. Roberts*
Affiliation:
University of Warwick
*
*Postal address: Coventry CV4 7AL, U.K.
**Email address: dootika@iitk.ac.in
*Postal address: Coventry CV4 7AL, U.K.
*Postal address: Coventry CV4 7AL, U.K.
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Abstract

The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis–Hastings (MH) algorithms. Recently, acceptance probabilities other than MH are being employed in problems with intractable target distributions. There are few resources available on tuning the Gaussian proposal distributions for this situation. We obtain optimal scaling results for a general class of acceptance functions, which includes Barker’s and lazy MH. In particular, optimal values for Barker’s algorithm are derived and found to be significantly different from that obtained for the MH algorithm. Our theoretical conclusions are supported by numerical simulations indicating that when the optimal proposal variance is unknown, tuning to the optimal acceptance probability remains an effective strategy.

Keywords

Barker’s acceptanceweak convergenceMetropolis–Hastingslazy MHtuning

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60F05: Central limit and other weak theorems
Type
Original Article
Information
Advances in Applied Probability , Volume 55 , Issue 2 , June 2023 , pp. 492 - 509
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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