Home > Research > Publications & Outputs > Merging MCMC subposteriors through Gaussian-Pro...

Links

Text available via DOI:

View graph of relations

Merging MCMC subposteriors through Gaussian-Process Approximations

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>03/2018
<mark>Journal</mark>Bayesian Analysis
Issue number2
Volume13
Number of pages24
Pages (from-to)507-530
Publication statusPublished
Early online date9/08/17
Original languageEnglish

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.