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Journal Articles ACM Transactions on Modeling and Computer Simulation Year : 2017

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

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Abstract

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.

Dates and versions

hal-01669115 , version 1 (20-12-2017)

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Cite

Pierre del Moral, Ajay Jasra, Kody J. H. Law, Yan Zhou. Multilevel Sequential Monte Carlo Samplers for Normalizing Constants. ACM Transactions on Modeling and Computer Simulation, 2017, 27 (3), pp.1 - 22. ⟨10.1145/3092841⟩. ⟨hal-01669115⟩
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