Journal article

The Block-Poisson Estimator for Optimally Tuned Exact Subsampling MCMC

M Quiroz, MN Tran, M Villani, R Kohn, KD Dang

Journal of Computational and Graphical Statistics | Published : 2021

Abstract

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-Poi..

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