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November 2017 Barker’s algorithm for Bayesian inference with intractable likelihoods
Flávio B. Gonçalves, Krzysztof Łatuszyński, Gareth O. Roberts
Braz. J. Probab. Stat. 31(4): 732-745 (November 2017). DOI: 10.1214/17-BJPS374

Abstract

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.

Citation

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Flávio B. Gonçalves. Krzysztof Łatuszyński. Gareth O. Roberts. "Barker’s algorithm for Bayesian inference with intractable likelihoods." Braz. J. Probab. Stat. 31 (4) 732 - 745, November 2017. https://doi.org/10.1214/17-BJPS374

Information

Received: 1 December 2016; Accepted: 1 August 2017; Published: November 2017
First available in Project Euclid: 15 December 2017

zbMATH: 1385.65013
MathSciNet: MR3738176
Digital Object Identifier: 10.1214/17-BJPS374

Keywords: 2-coin algorithm , Barker’s algorithm , Bayesian inference , Bernoulli factory , intractable likelihood , Stochastic differential equations , Wright–Fisher diffusion

Rights: Copyright © 2017 Brazilian Statistical Association

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Vol.31 • No. 4 • November 2017
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