Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions
We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs to noncompact statespaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Univ. of Bordeaux (France)
 National Univ. of Singapore (Singapore)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Stochastic Analysis and Applications
 Additional Journal Information:
 Journal Volume: 35; Journal Issue: 3; Journal ID: ISSN 07362994
 Research Org:
 Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1361332
Del Moral, Pierre, Jasra, Ajay, and Law, Kody J. H.. Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions. United States: N. p.,
Web. doi:10.1080/07362994.2016.1272421.
Del Moral, Pierre, Jasra, Ajay, & Law, Kody J. H.. Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions. United States. doi:10.1080/07362994.2016.1272421.
Del Moral, Pierre, Jasra, Ajay, and Law, Kody J. H.. 2017.
"Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions". United States.
doi:10.1080/07362994.2016.1272421. https://www.osti.gov/servlets/purl/1361332.
@article{osti_1361332,
title = {Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions},
author = {Del Moral, Pierre and Jasra, Ajay and Law, Kody J. H.},
abstractNote = {We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs to noncompact statespaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.},
doi = {10.1080/07362994.2016.1272421},
journal = {Stochastic Analysis and Applications},
number = 3,
volume = 35,
place = {United States},
year = {2017},
month = {1}
}