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Barker's algorithm for Bayesian inference with intractable likelihoods

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Goncalves, Flavio B., Latuszynski, Krzysztof and Roberts, Gareth O. (2017) Barker's algorithm for Bayesian inference with intractable likelihoods. Brazilian Journal of Probability and Statistics, 31 (4). pp. 732-745. doi:10.1214/17-BJPS374 ISSN 0103-0752.

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Official URL: https://doi.org/10.1214/17-BJPS374

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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 Goncalves et al. (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.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title: Brazilian Journal of Probability and Statistics
Publisher: Duke University Press
ISSN: 0103-0752
Official Date: 15 December 2017
Dates:
DateEvent
15 December 2017Published
31 October 2017Accepted
Volume: 31
Number: 4
Page Range: pp. 732-745
DOI: 10.1214/17-BJPS374
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 6 December 2017
Date of first compliant Open Access: 21 May 2018
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