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

High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk 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...

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Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Schmon, Sebastian M, Gagnon, Philippe
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic properties
Convergence
Density
Guidelines
Random walk
Scaling
Tuning
Online Access:Get full text
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Summary:High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk 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 parameter-dimension-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.
ISSN:2331-8422