Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm

Jingyi Zhang; James C. Spall

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arXiv · 2511.10967

Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm

Jingyi Zhang·James C. Spall

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Abstract

The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important statistical property for both theory and implementation-remains less understood. In this work, we provide new theoretical insights into the scalar case, focusing primarily on symmetric unimodal target distributions with symmetric random walk proposals, where we also establish an optimal proposal design. In addition, we derive some more general results beyond this setting. For the high-dimensional case, we relate the covariance matrix to the classical 0.23 average acceptance rate tuning criterion.

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BibTeX RIS

Jingyi Zhang, James C. Spall. 2025-11-14. Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm. https://arxiv.org/abs/2511.10967

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