Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals
In this article we develop a new sequential Monte Carlo method for multilevel Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an infinite-dimensional and noncompact space—as produced, for example, by a Baye...
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| Format: | Article |
| Language: | English |
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Society for Industrial & Applied Mathematics (SIAM)
2020
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| Online Access: | https://hdl.handle.net/1721.1/126540 |
| _version_ | 1826199465800761344 |
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| author | Marzouk, Youssef M |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Marzouk, Youssef M |
| author_sort | Marzouk, Youssef M |
| collection | MIT |
| description | In this article we develop a new sequential Monte Carlo method for multilevel Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an infinite-dimensional and noncompact space—as produced, for example, by a Bayesian inverse problem with a Gaussian random field prior. Under suitable assumptions the MLSMC method has the optimal O(ε−2) bound on the cost to obtain a mean-square error of O(ε2). The algorithm is accelerated by dimension-independent likelihood-informed proposals [T. Cui, K. J. Law, and Y. M. Marzouk, (2016), J. Comput. Phys., 304, pp. 109–137] designed for Gaussian priors, leveraging a novel variation which uses empirical covariance information in lieu of Hessian information, hence eliminating the requirement for gradient evaluations. The efficiency of the algorithm is illustrated on two examples: (i) inversion of noisy pressure measurements in a PDE model of Darcy flow to recover the posterior distribution of the permeability field and (ii) inversion of noisy measurements of the solution of an SDE to recover the posterior path measure. |
| first_indexed | 2024-09-23T11:20:40Z |
| format | Article |
| id | mit-1721.1/126540 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:20:40Z |
| publishDate | 2020 |
| publisher | Society for Industrial & Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/1265402022-09-27T18:52:49Z Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals Marzouk, Youssef M Massachusetts Institute of Technology. Department of Aeronautics and Astronautics In this article we develop a new sequential Monte Carlo method for multilevel Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an infinite-dimensional and noncompact space—as produced, for example, by a Bayesian inverse problem with a Gaussian random field prior. Under suitable assumptions the MLSMC method has the optimal O(ε−2) bound on the cost to obtain a mean-square error of O(ε2). The algorithm is accelerated by dimension-independent likelihood-informed proposals [T. Cui, K. J. Law, and Y. M. Marzouk, (2016), J. Comput. Phys., 304, pp. 109–137] designed for Gaussian priors, leveraging a novel variation which uses empirical covariance information in lieu of Hessian information, hence eliminating the requirement for gradient evaluations. The efficiency of the algorithm is illustrated on two examples: (i) inversion of noisy pressure measurements in a PDE model of Darcy flow to recover the posterior distribution of the permeability field and (ii) inversion of noisy measurements of the solution of an SDE to recover the posterior path measure. United States. Department of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0009297 (DiaMond MMICC)) 2020-08-12T14:23:05Z 2020-08-12T14:23:05Z 2018-06 2017-03 2019-10-29T18:22:29Z Article http://purl.org/eprint/type/JournalArticle 2166-2525 https://hdl.handle.net/1721.1/126540 Beskos, Alexandros et al. “Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals.” SIAM/ASA journal on uncertainty quantification, vol. 6, no. 2, 2018, pp. 762-786 © 2018 The Author(s) en 10.1137/17M1120993 SIAM/ASA journal on uncertainty quantification Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial & Applied Mathematics (SIAM) SIAM |
| spellingShingle | Marzouk, Youssef M Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals |
| title | Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals |
| title_full | Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals |
| title_fullStr | Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals |
| title_full_unstemmed | Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals |
| title_short | Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals |
| title_sort | multilevel sequential monte carlo with dimension independent likelihood informed proposals |
| url | https://hdl.handle.net/1721.1/126540 |
| work_keys_str_mv | AT marzoukyoussefm multilevelsequentialmontecarlowithdimensionindependentlikelihoodinformedproposals |