Optimal scaling of random-walk metropolis algorithms on general target distributions
One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arisin...
| Hauptverfasser: | , , |
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| Format: | Journal article |
| Sprache: | English |
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Elsevier
2020
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| _version_ | 1826310358695936000 |
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| author | Yang, J Roberts, GO Rosenthal, JS |
| author_facet | Yang, J Roberts, GO Rosenthal, JS |
| author_sort | Yang, J |
| collection | OXFORD |
| description | One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions. |
| first_indexed | 2024-03-07T07:49:15Z |
| format | Journal article |
| id | oxford-uuid:f2472c8e-dc3c-4a45-87d1-d7d60a63b3c8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:49:15Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:f2472c8e-dc3c-4a45-87d1-d7d60a63b3c82023-06-30T15:50:35ZOptimal scaling of random-walk metropolis algorithms on general target distributionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f2472c8e-dc3c-4a45-87d1-d7d60a63b3c8EnglishSymplectic ElementsElsevier2020Yang, JRoberts, GORosenthal, JSOne main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions. |
| spellingShingle | Yang, J Roberts, GO Rosenthal, JS Optimal scaling of random-walk metropolis algorithms on general target distributions |
| title | Optimal scaling of random-walk metropolis algorithms on general target distributions |
| title_full | Optimal scaling of random-walk metropolis algorithms on general target distributions |
| title_fullStr | Optimal scaling of random-walk metropolis algorithms on general target distributions |
| title_full_unstemmed | Optimal scaling of random-walk metropolis algorithms on general target distributions |
| title_short | Optimal scaling of random-walk metropolis algorithms on general target distributions |
| title_sort | optimal scaling of random walk metropolis algorithms on general target distributions |
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