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June 2018 Merging MCMC Subposteriors through Gaussian-Process Approximations
Christopher Nemeth, Chris Sherlock
Bayesian Anal. 13(2): 507-530 (June 2018). DOI: 10.1214/17-BA1063

Abstract

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run independent MCMC algorithms targeting the corresponding subposterior, can spread the computational burden across a number of separate computer cores. The challenge with such strategies is in recombining the subposteriors to approximate the full posterior. By creating a Gaussian-process approximation for each log-subposterior density we create a tractable approximation for the full posterior. This approximation is exploited through three methodologies: firstly a Hamiltonian Monte Carlo algorithm targeting the expectation of the posterior density provides a sample from an approximation to the posterior; secondly, evaluating the true posterior at the sampled points leads to an importance sampler that, asymptotically, targets the true posterior expectations; finally, an alternative importance sampler uses the full Gaussian-process distribution of the approximation to the log-posterior density to re-weight any initial sample and provide both an estimate of the posterior expectation and a measure of the uncertainty in it.

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Christopher Nemeth. Chris Sherlock. "Merging MCMC Subposteriors through Gaussian-Process Approximations." Bayesian Anal. 13 (2) 507 - 530, June 2018. https://doi.org/10.1214/17-BA1063

Information

Published: June 2018
First available in Project Euclid: 9 August 2017

zbMATH: 06989958
MathSciNet: MR3780433
Digital Object Identifier: 10.1214/17-BA1063

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Vol.13 • No. 2 • June 2018
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