Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915808228147200 |
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| author | Milinanni, Federica Nyquist, Pierre |
| author_facet | Milinanni, Federica Nyquist, Pierre |
| contents | In this paper, we prove large deviation principles for the empirical measures associated with the Independent Metropolis Hastings (IMH) sampler and the Metropolis-adjusted Langevin Algorithm (MALA). These are the first large deviation results for empirical measures of Markov chains arising from specific Metropolis-Hastings methods on a continuous state space. Moreover, we show that the existing large deviation framework, that we developed in a previous work (Milinanni and Nyquist, 2024), does not cover the Random Walk Metropolis sampler, even in cases when the underlying Markov chain is geometrically ergodic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm Milinanni, Federica Nyquist, Pierre Probability Statistics Theory 60F10, 65C05, secondary 60G57, 60J05 In this paper, we prove large deviation principles for the empirical measures associated with the Independent Metropolis Hastings (IMH) sampler and the Metropolis-adjusted Langevin Algorithm (MALA). These are the first large deviation results for empirical measures of Markov chains arising from specific Metropolis-Hastings methods on a continuous state space. Moreover, we show that the existing large deviation framework, that we developed in a previous work (Milinanni and Nyquist, 2024), does not cover the Random Walk Metropolis sampler, even in cases when the underlying Markov chain is geometrically ergodic. |
| title | Large deviations for Independent Metropolis Hastings and Metropolis-adjusted Langevin algorithm |
| topic | Probability Statistics Theory 60F10, 65C05, secondary 60G57, 60J05 |
| url | https://arxiv.org/abs/2403.08691 |