The Block-Poisson Estimator for Optimally Tuned Exact Subsampling MCMC

Speeding up Markov chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and graphical statistics 2021-10, Vol.30 (4), p.877-888
Main Authors: Quiroz, Matias, Tran, Minh-Ngoc, Villani, Mattias, Kohn, Robert, Dang, Khue-Dung
Format: Article
Language:English
Subjects:
Algorithms
Bayesian inference
Control variates
Data subsampling
Estimates
Exact inference
Importance sampling
Markov chains
Optimization
Parameter estimation
Poisson estimator
Pseudo-marginal MCMC
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Speeding up Markov chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favorably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature. Supplementary materials for this article are available online.
ISSN:1061-8600
1537-2715
1537-2715
DOI:10.1080/10618600.2021.1917420