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Efficient Bernoulli factory MCMC for intractable likelihoods
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Vats, Dootika, Gonçalves, Flavio B., Latuszynski , Krzysztof and Roberts, Gareth O. (2022) Efficient Bernoulli factory MCMC for intractable likelihoods. Biometrika, 109 (2). pp. 369-385. doi:10.1093/biomet/asab031 ISSN 0006-3444.
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Official URL: https://doi.org/10.1093/biomet/asab031
Abstract
Accept-reject based Markov chain Monte Carlo algorithms have traditionally utilized acceptance probabilities that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is rendered almost useless in Bayesian posteriors with unknown functional forms. We introduce a new family of Markov chain Monte Carlo acceptance probabilities that has the distinguishing feature of not being a function of the ratio of the target density at the two points. We present two stable Bernoulli factories that generate events within this class of acceptance probabilities. The efficiency of our methods rely on obtaining reasonable local upper or lower bounds on the target density and we present two classes of problems where such bounds are viable: Bayesian inference for diffusions and Markov chain Monte Carlo on constrained spaces. The resulting portkey Barker’s algorithms are exact and computationally more efficient that the current state-of-the-art.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Biometrika | ||||||||
Publisher: | Biometrika Trust | ||||||||
ISSN: | 0006-3444 | ||||||||
Official Date: | June 2022 | ||||||||
Dates: |
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Volume: | 109 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 369-385 | ||||||||
DOI: | 10.1093/biomet/asab031 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in Biometrika following peer review. The version of record D Vats, F B Gonçalves, K Łatuszyński, G O Roberts, Efficient Bernoulli factory MCMC for intractable posteriors, Biometrika, 2021;, asab031 is available online at: https://doi.org/10.1093/biomet/asab031 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 7 May 2021 | ||||||||
Date of first compliant Open Access: | 11 June 2022 | ||||||||
Related URLs: | |||||||||
Open Access Version: |
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