Journal
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
Volume 31, Issue 3, Pages 695-708Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/10618600.2022.2034637
Keywords
Bayesian computation; Importance sampling; Monte Carlo; Quasi-Monte Carlo; Resampling; Support points
Categories
Funding
- U.S. National Science Foundation [CMMI-1921646]
- NSF CSSI Frameworks grant [2004571]
Ask authors/readers for more resources
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 that adapts a population of proposals to generate weighted samples approximating the target distribution. To address computational limitations of PMC when evaluating the target distribution is expensive, we propose a new method, Population Quasi-Monte Carlo (PQMC), which incorporates Quasi-Monte Carlo ideas and introduces importance support points resampling and efficient covariance adaptation strategies within the sampling and adaptation steps of PMC.
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available