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

Schmon, Sebastian M.; Gagnon, Philippe

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Authors

Sebastian M. Schmon

Philippe Gagnon



Abstract

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.

Citation

Schmon, S. M., & Gagnon, P. (2022). Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptotics. Statistics and Computing, 32(2), Article 28. https://doi.org/10.1007/s11222-022-10080-8

Journal Article Type Article
Acceptance Date Jan 19, 2022
Online Publication Date Feb 18, 2022
Publication Date 2022
Deposit Date Mar 3, 2022
Publicly Available Date May 11, 2022
Journal Statistics and Computing
Print ISSN 0960-3174
Electronic ISSN 1573-1375
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 32
Issue 2
Article Number 28
DOI https://doi.org/10.1007/s11222-022-10080-8

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright 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 http://creativecommons.org/licenses/by/4.0/.




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