Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

Pierre del Moral (1) , Ajay Jasra (2) , Kody Law (3) , Yan Zhou (4)

1 CQFD - Quality control and dynamic reliability
2 Department of Computing [London]
3 Department of Mathematics and Statistics [University of Massachusetts]
4 BGI - Beijing Genomics Institute [Shenzhen]

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 esti-mators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for the example of identifying a parametrized permeability in an elliptic equation given point-wise observations of the pressure.

Mots clés: Multi-Level Monte Carlo; Sequential Monte Carlo; Bayesian Inverse Problems

Domaines: Probabilités [math.PR]

Pierre del Moral, Ajay Jasra, Kody Law, Yan Zhou. Multilevel Sequential Monte Carlo Samplers for Normalizing Constants. [Research Report] Arxiv. 2016. ⟨hal-01593880⟩