Population Quasi-Monte Carlo

Abstract

Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which adapts a population of proposals to generate weighted samples that approximate the target distribution. When the target distribution is expensive to evaluate, PMC may encounter computational limitations since it requires many evaluations of the target distribution. To address this, we propose a new method, Population Quasi-Monte Carlo (PQMC), which integrates Quasi-Monte Carlo ideas within the sampling and adaptation steps of PMC. A key novelty in PQMC is the idea of importance support points resampling, a deterministic method for finding an “optimal” subsample from the weighted proposal samples. Moreover, within the PQMC framework, we develop an efficient covariance adaptation strategy for multivariate normal proposals. Finally, a new set of correction weights is introduced for the weighted PMC estimator to improve the efficiency from the standard PMC estimator. We demonstrate the improved empirical performance of PQMC over PMC in extensive numerical simulations and a friction drilling application. Supplementary materials for this article are available online.