Accelerating Pseudo-Marginal MCMC using Gaussian Processes

Drovandi, Christopher C., Moores, Matthew T., & Boys, Richard J. (2015) Accelerating Pseudo-Marginal MCMC using Gaussian Processes. [Working Paper] (Unpublished)

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Abstract

Pseudo-marginal methods such as the grouped independence Metropolis-Hastings (GIMH) and Markov chain within Metropolis (MCWM) algorithms have been introduced in the literature as an approach 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 less theoretical support. In this paper we propose to use Gaussian processes (GP) to accelerate the GIMH method, whilst using a short pilot run of MCWM to train the GP. Our new method, GP-GIMH, is illustrated on simulated data from a stochastic volatility and a gene network model.

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ID Code: 90973
Item Type: Working Paper
Refereed: No
Keywords: Gaussian processes, likelihood-free methods, Markov processes, particle Markov chain Monte Carlo, pseudo-marginal methods, state space models
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Statistical Theory (010405)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Stochastic Analysis and Modelling (010406)
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 The Author(s)
Deposited On: 02 Dec 2015 23:52
Last Modified: 05 Dec 2015 03:15

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