Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912931204038656 |
|---|---|
| author | Zhang, Jingyi Spall, James C. |
| author_facet | Zhang, Jingyi Spall, James C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm Zhang, Jingyi Spall, James C. Computation Optimization and Control Statistics Theory 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. |
| title | Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm |
| topic | Computation Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2511.10967 |