DEL MORAL, Pierre; JASRA, Ajay; LAW, Kody J. H.; ZHOU, Yan

doi:10.1145/3092841

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DEL MORAL, Pierre
Quality control and dynamic reliability [CQFD]

JASRA, Ajay
National University of Singapore [NUS]

LAW, Kody J. H.
Oak Ridge National Laboratory [Oak Ridge] [ORNL]

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ACM Transactions on Modeling and Computer Simulation. 2017-09-07, vol. 27, n° 3, p. 1 - 22

Association for Computing Machinery

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This article considers the Sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic Partial Differential Equations (PDEs). The examples involve the inversion of observations of the solution of (i) a one-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a two-dimensional Poisson equation to infer the external forcing.< Réduire

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Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

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