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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
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 | |||||||||
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| 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: |
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| 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: |
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