期刊
BIOMETRIKA
卷 109, 期 2, 页码 369-385出版社
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asab031
关键词
Barker's method; Bernoulli factory; Intractable likelihood; Markov chain Monte Carlo
资金
- National Science Foundation [DMS/1703691]
- FAPEMIG
- CNPq
- University of Warwick
- Royal Society University Research Fellowship
- EPSRC [EP/K014463/1]
- Bayes for Health [EP/R018561/1]
- CoSInES [EP/R034710/1]
The paper introduces a new family of Markov chain Monte Carlo acceptance probabilities that are not based on the ratio of the target density at contested points, providing two stable Bernoulli factories. The efficiency of the methods relies on obtaining reasonable local upper or lower bounds on the target density, applicable to Bayesian inference for diffusions and Markov chain Monte Carlo on constrained spaces. The resulting Barker's algorithms are exact and computationally more efficient than current state-of-the-art methods.
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 relies 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.
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