Analysis of Multiple-try Metropolis via Poincaré inequalities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912714280927232 |
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| author | Caprio, Rocco Power, Sam Wang, Andi Q. |
| author_facet | Caprio, Rocco Power, Sam Wang, Andi Q. |
| contents | We study the Multiple-try Metropolis algorithm using the framework of Poincaré inequalities. We describe the Multiple-try Metropolis as an auxiliary variable implementation of a resampling approximation to an ideal Metropolis--Hastings algorithm. Under suitable moment conditions on the importance weights, we derive explicit Poincaré comparison results between the Multiple-try algorithm and the ideal algorithm. We characterize the spectral gap of the latter, and finally in the Gaussian case prove explicit non-asymptotic convergence bounds for Multiple-try Metropolis by comparison. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of Multiple-try Metropolis via Poincaré inequalities Caprio, Rocco Power, Sam Wang, Andi Q. Computation Probability We study the Multiple-try Metropolis algorithm using the framework of Poincaré inequalities. We describe the Multiple-try Metropolis as an auxiliary variable implementation of a resampling approximation to an ideal Metropolis--Hastings algorithm. Under suitable moment conditions on the importance weights, we derive explicit Poincaré comparison results between the Multiple-try algorithm and the ideal algorithm. We characterize the spectral gap of the latter, and finally in the Gaussian case prove explicit non-asymptotic convergence bounds for Multiple-try Metropolis by comparison. |
| title | Analysis of Multiple-try Metropolis via Poincaré inequalities |
| topic | Computation Probability |
| url | https://arxiv.org/abs/2504.18409 |