Multilevel Sequential Monte Carlo Samplers for Normalizing Constants
Computation
2016-03-04 v1 Numerical Analysis
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 the example of identifying a parametrized permeability in an elliptic equation given point-wise observations of the pressure.
Cite
@article{arxiv.1603.01136,
title = {Multilevel Sequential Monte Carlo Samplers for Normalizing Constants},
author = {Pierre Del Moral and Ajay Jasra and Kody Law and Yan Zhou},
journal= {arXiv preprint arXiv:1603.01136},
year = {2016}
}