Merging MCMC subposteriors through Gaussian-Process Approximations

Nemeth, Christopher and Sherlock, Christopher Gerrard (2018) Merging MCMC subposteriors through Gaussian-Process Approximations. Bayesian Analysis, 13 (2). pp. 507-530. ISSN 1936-0975

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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.

Item Type:
Journal Article
Journal or Publication Title:
Bayesian Analysis
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
79862
Deposited By:
Deposited On:
06 Jun 2016 15:36
Refereed?:
Yes
Published?:
Published
Last Modified:
24 Nov 2020 04:17