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Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptotics

Schmon, Sebastian M. and Gagnon, Philippe (2022) 'Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptotics.', Statistics and Computing, 32 (2). p. 28.


High-dimensional limit theorems have been useful to derive tuning rules for finding the optimal scaling in randomwalk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the target density is typically assumed to be of a product form. Users may thus doubt the validity of such tuning rules in practical applications. In this paper, we shed some light on optimal-scaling problems from a different perspective, namely a large-sample one. This allows to prove weak convergence results under realistic assumptions and to propose novel parameterdimension- dependent tuning guidelines. The proposed guidelines are consistent with previous ones when the target density is close to having a product form, and the results highlight that the correlation structure has to be accounted for to avoid performance deterioration if that is not the case, while justifying the use of a natural (asymptotically exact) approximation to the correlation matrix that can be employed for the very first algorithm run.

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Publisher statement:This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Date accepted:19 January 2022
Date deposited:03 March 2022
Date of first online publication:18 February 2022
Date first made open access:11 May 2022

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