Brazilian Journal of Probability and Statistics

Barker’s algorithm for Bayesian inference with intractable likelihoods

Flávio B. Gonçalves, Krzysztof Łatuszyński, and Gareth O. Roberts

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In this expository paper, we abstract and describe a simple MCMC scheme for sampling from intractable target densities. The approach has been introduced in Gonçalves, Łatuszyński and Roberts (2017a) in the specific context of jump-diffusions, and is based on the Barker’s algorithm paired with a simple Bernoulli factory type scheme, the so called 2-coin algorithm. In many settings, it is an alternative to standard Metropolis–Hastings pseudo-marginal method for simulating from intractable target densities. Although Barker’s is well known to be slightly less efficient than Metropolis–Hastings, the key advantage of our approach is that it allows to implement the “marginal Barker’s” instead of the extended state space pseudo-marginal Metropolis–Hastings, owing to the special form of the accept/reject probability. We shall illustrate our methodology in the context of Bayesian inference for discretely observed Wright–Fisher family of diffusions.

Article information

Braz. J. Probab. Stat., Volume 31, Number 4 (2017), 732-745.

Received: December 2016
Accepted: August 2017
First available in Project Euclid: 15 December 2017

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Zentralblatt MATH identifier

Intractable likelihood Bayesian inference Barker’s algorithm Bernoulli factory 2-coin algorithm stochastic differential equations Wright–Fisher diffusion


Gonçalves, Flávio B.; Łatuszyński, Krzysztof; Roberts, Gareth O. Barker’s algorithm for Bayesian inference with intractable likelihoods. Braz. J. Probab. Stat. 31 (2017), no. 4, 732--745. doi:10.1214/17-BJPS374.

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