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

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

doi:10.1080/07362994.2016.1272421

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

Journal Article · Mon Jan 09 00:00:00 EST 2017 · Stochastic Analysis and Applications

DOI:https://doi.org/10.1080/07362994.2016.1272421· OSTI ID:1361332

Del Moral, Pierre ^[1]; Jasra, Ajay ^[2]; Law, Kody J. H. ^[3]

Univ. of Bordeaux (France)
National Univ. of Singapore (Singapore)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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 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.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1361332

Journal Information:: Stochastic Analysis and Applications, Vol. 35, Issue 3; ISSN 0736-2994

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (21)

On adaptive resampling strategies for sequential Monte Carlo methods Del Moral, Pierre; Doucet, Arnaud; Jasra, Ajay Bernoulli, Vol. 18, Issue 1 https://doi.org/10.3150/10-BEJ335	journal	February 2012
Multilevel Monte Carlo Path Simulation Giles, Michael B. Operations Research, Vol. 56, Issue 3 https://doi.org/10.1287/opre.1070.0496	journal	June 2008
Stability properties of some particle filters Whiteley, Nick The Annals of Applied Probability, Vol. 23, Issue 6 https://doi.org/10.1214/12-AAP909	journal	December 2013
Feynman-Kac Formulae Del Moral, Pierre Probability and its Applications https://doi.org/10.1007/978-1-4684-9393-1	book	January 2004
Monte Carlo Complexity of Global Solution of Integral Equations Heinrich, S. Journal of Complexity, Vol. 14, Issue 2 https://doi.org/10.1006/jcom.1998.0471	journal	June 1998
Complexity analysis of accelerated MCMC methods for Bayesian inversion Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. Inverse Problems, Vol. 29, Issue 8 https://doi.org/10.1088/0266-5611/29/8/085010	journal	July 2013
Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes Kontoyiannis, Ioannis; Meyn, Sean Electronic Journal of Probability, Vol. 10, Issue 0 https://doi.org/10.1214/EJP.v10-231	journal	January 2005
Sequential Monte Carlo Samplers: Error Bounds and Insensitivity to Initial Conditions Whiteley, Nick Stochastic Analysis and Applications, Vol. 30, Issue 5 https://doi.org/10.1080/07362994.2012.684323	journal	September 2012
Multilevel sequential Monte Carlo samplers Beskos, Alexandros; Jasra, Ajay; Law, Kody Stochastic Processes and their Applications, Vol. 127, Issue 5 https://doi.org/10.1016/j.spa.2016.08.004	journal	May 2017
Forward and Inverse Uncertainty Quantification Using Multilevel Monte Carlo Algorithms for an Elliptic Nonlocal Equation Jasra, Ajay; Law, Kody J. H.; Zhou, Yan International Journal for Uncertainty Quantification, Vol. 6, Issue 6 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2016018661	journal	January 2016
On the Behaviour of the Backward Interpretation of Feynman-Kac Formulae Under Verifiable Conditions Jasra, Ajay Journal of Applied Probability, Vol. 52, Issue 02 https://doi.org/10.1017/S002190020001250X	journal	June 2015
Linear variance bounds for particle approximations of time-homogeneous Feynman–Kac formulae Whiteley, Nick; Kantas, Nikolas; Jasra, Ajay Stochastic Processes and their Applications, Vol. 122, Issue 4 https://doi.org/10.1016/j.spa.2012.02.002	journal	April 2012
Sequential Monte Carlo samplers Del Moral, Pierre; Doucet, Arnaud; Jasra, Ajay Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 68, Issue 3 https://doi.org/10.1111/j.1467-9868.2006.00553.x	journal	June 2006
On the Behaviour of the Backward Interpretation of Feynman-Kac Formulae Under Verifiable Conditions Jasra, Ajay Journal of Applied Probability, Vol. 52, Issue 2 https://doi.org/10.1239/jap/1437658602	journal	June 2015
Sequential Monte Carlo samplers: error bounds and insensitivity to initial conditions Whiteley, Nick arXiv https://doi.org/10.48550/arxiv.1103.3970	preprint	January 2011
Linear Variance Bounds for Particle Approximations of Time-Homogeneous Feynman-Kac Formulae Whiteley, Nick; Kantas, Nikolas; Jasra, Ajay arXiv https://doi.org/10.48550/arxiv.1108.3988	text	January 2011
Stability properties of some particle filters Whiteley, Nick arXiv https://doi.org/10.48550/arxiv.1109.6779	text	January 2011
On adaptive resampling strategies for sequential Monte Carlo methods Del Moral, Pierre; Doucet, Arnaud; Jasra, Ajay arXiv https://doi.org/10.48550/arxiv.1203.0464	text	January 2012
Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. arXiv https://doi.org/10.48550/arxiv.1207.2411	preprint	January 2012
Forward and Inverse Uncertainty Quantification using Multilevel Monte Carlo Algorithms for an Elliptic Nonlocal Equation Jasra, Ajay; Law, Kody; Zhou, Yan arXiv https://doi.org/10.48550/arxiv.1603.06381	preprint	January 2016
Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes Kontoyiannis, Ioannis; Meyn, S. P. arXiv https://doi.org/10.48550/arxiv.math/0509310	text	January 2005

Cited By (2)

Multilevel Monte Carlo in approximate Bayesian computation Jasra, Ajay; Jo, Seongil; Nott, David Stochastic Analysis and Applications, Vol. 37, Issue 3 https://doi.org/10.1080/07362994.2019.1566006	journal	January 2019
Multilevel Monte Carlo in Approximate Bayesian Computation Jasra, Ajay; Jo, Seongil; Nott, David arXiv https://doi.org/10.48550/arxiv.1702.03628	preprint	January 2017

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