Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

Pierre Del Moral, Ajay Jasra, Kody J.H. Law

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this article, we consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This is a technique 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 non-compact state-spaces. 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.

    Original languageEnglish
    Pages (from-to)478-498
    Number of pages21
    JournalStochastic Analysis and Applications
    Volume35
    Issue number3
    Early online date9 Jan 2017
    DOIs
    Publication statusPublished - 2017

    Keywords

    • drift conditions
    • Multilevel Monte Carlo
    • sequential Monte Carlo

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