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Accelerating pseudo-marginal MCMC using Gaussian processes

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Drovandi, Christopher C., Moores, Matthew T. and Boys, Richard J. (2018) Accelerating pseudo-marginal MCMC using Gaussian processes. Computational Statistics & Data Analysis, 118 . doi:10.1016/j.csda.2017.09.002 ISSN 0167-9473.

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Official URL: http://dx.doi.org/10.1016/j.csda.2017.09.002

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Abstract

The grouped independence Metropolis–Hastings (GIMH) and Markov chain within Metropolis (MCWM) algorithms are pseudo-marginal methods used to perform Bayesian inference in latent variable models. These methods replace intractable likelihood calculations with unbiased estimates within Markov chain Monte Carlo algorithms. The GIMH method has the posterior of interest as its limiting distribution, but suffers from poor mixing if it is too computationally intensive to obtain high-precision likelihood estimates. The MCWM algorithm has better mixing properties, but tends to give conservative approximations of the posterior and is still expensive. A new method is developed to accelerate the GIMH method by using a Gaussian process (GP) approximation to the log-likelihood and train this GP using a short pilot run of the MCWM algorithm. This new method called GP-GIMH is illustrated on simulated data from a stochastic volatility and a gene network model. The new approach produces reasonable posterior approximations in these examples with at least an order of magnitude improvement in computing time. Code to implement the method for the gene network example can be found at http://www.runmycode.org/companion/view/2663.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Gaussian processes, Markov processes, Monte Carlo method
Journal or Publication Title: Computational Statistics & Data Analysis
Publisher: Elsevier Science Ltd
ISSN: 0167-9473
Official Date: February 2018
Dates:
DateEvent
February 2018Published
14 September 2017Available
3 September 2017Accepted
Volume: 118
DOI: 10.1016/j.csda.2017.09.002
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 26 September 2017
Date of first compliant Open Access: 14 September 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
DE160100741Australian Research Councilhttp://dx.doi.org/10.13039/501100000923
EP/K014463/1Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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