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Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo

Boom, Willem van den; Jasra, Ajay; De Iorio, Maria; Beskos, Alexandros; Eriksson, Johan G; (2022) Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo. Statistics and Computing , 32 , Article 36. 10.1007/s11222-022-10093-3. Green open access

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Abstract

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallelisable computation on HPC and cloud environments. Another concern is the identification of the bias and Monte Carlo error of produced averages. The above have prompted the recent development of fully (`embarrassingly') parallelisable unbiased Monte Carlo methodology based on couplings of MCMC algorithms. A caveat is that formulation of effective couplings is typically not trivial and requires model-specific technical effort. We propose couplings of sequential Monte Carlo (SMC) by considering adaptive SMC to approximate complex, high-dimensional posteriors combined with recent advances in unbiased estimation for state-space models. Coupling is then achieved at the SMC level and is, in general, not problem-specific. The resulting methodology enjoys desirable theoretical properties. We illustrate the effectiveness of the algorithm via application to two statistical models in high dimensions: (i) horseshoe regression; (ii) Gaussian graphical models.

Type: Article
Title: Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11222-022-10093-3
Publisher version: https://doi.org/10.1007/s11222-022-10093-3
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Adaptive sequential Monte Carlo, Coupling, Embarrassingly parallel computing, Gaussian graphical model, Particle filter, Unbiased MCMC
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10145985
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