Multilevel sequential Monte Carlo samplers

Beskos, Alexandros; Jasra, Ajay; Law, Kody; Tempone, Raul; Zhou, Yan

doi:10.1016/j.spa.2016.08.004

Title: Multilevel sequential Monte Carlo samplers

Journal Article · Wed Aug 24 00:00:00 EDT 2016 · Stochastic Processes and Their Applications

DOI:https://doi.org/10.1016/j.spa.2016.08.004· OSTI ID:1302922

Beskos, Alexandros ^[1]; Jasra, Ajay ^[2]; Law, Kody ^[3]; Tempone, Raul ^[4]; Zhou, Yan ^[2]

Univ. College London, London (United Kingdom). Dept. of Statistical Science
National Univ. of Singapore (Singapore). Dept. of Statistics & Applied Probability
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)

Here, we study the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level h_L. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levels $${\infty}$$ >h₀>h₁...>h_L. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. In conclusion, it is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC05-00OR22725; R-155-000-143-112

OSTI ID:: 1302922

Journal Information:: Stochastic Processes and Their Applications, Journal Name: Stochastic Processes and Their Applications; ISSN 0304-4149

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 44 works

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