Rao-Blackwellised parallel MCMC

Tobias Schwedes, Ben Calderhead
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3448-3456, 2021.

Abstract

Multiple proposal Markov chain Monte Carlo (MP-MCMC) as introduced in Calderhead (2014) allow for computationally efficient and parallelisable inference, whereby multiple states are proposed and computed simultaneously. In this paper, we improve the resulting integral estimators by sequentially using the multiple states within a Rao-Blackwellised estimator. We further propose a novel adaptive Rao-Blackwellised MP-MCMC algorithm, which generalises the adaptive MCMC algorithm introduced by Haario et al. (2001) to allow for multiple proposals. We prove its asymptotic unbiasedness, and demonstrate significant improvements in sampling efficiency through numerical studies.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-schwedes21a, title = { Rao-Blackwellised parallel MCMC }, author = {Schwedes, Tobias and Calderhead, Ben}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3448--3456}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/schwedes21a/schwedes21a.pdf}, url = {https://proceedings.mlr.press/v130/schwedes21a.html}, abstract = { Multiple proposal Markov chain Monte Carlo (MP-MCMC) as introduced in Calderhead (2014) allow for computationally efficient and parallelisable inference, whereby multiple states are proposed and computed simultaneously. In this paper, we improve the resulting integral estimators by sequentially using the multiple states within a Rao-Blackwellised estimator. We further propose a novel adaptive Rao-Blackwellised MP-MCMC algorithm, which generalises the adaptive MCMC algorithm introduced by Haario et al. (2001) to allow for multiple proposals. We prove its asymptotic unbiasedness, and demonstrate significant improvements in sampling efficiency through numerical studies. } }
Endnote
%0 Conference Paper %T Rao-Blackwellised parallel MCMC %A Tobias Schwedes %A Ben Calderhead %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-schwedes21a %I PMLR %P 3448--3456 %U https://proceedings.mlr.press/v130/schwedes21a.html %V 130 %X Multiple proposal Markov chain Monte Carlo (MP-MCMC) as introduced in Calderhead (2014) allow for computationally efficient and parallelisable inference, whereby multiple states are proposed and computed simultaneously. In this paper, we improve the resulting integral estimators by sequentially using the multiple states within a Rao-Blackwellised estimator. We further propose a novel adaptive Rao-Blackwellised MP-MCMC algorithm, which generalises the adaptive MCMC algorithm introduced by Haario et al. (2001) to allow for multiple proposals. We prove its asymptotic unbiasedness, and demonstrate significant improvements in sampling efficiency through numerical studies.
APA
Schwedes, T. & Calderhead, B.. (2021). Rao-Blackwellised parallel MCMC . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3448-3456 Available from https://proceedings.mlr.press/v130/schwedes21a.html.

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