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Barker’s algorithm for Bayesian inference with intractable likelihoods. (English) Zbl 1385.65013

Summary: In this expository paper, we abstract and describe a simple MCMC scheme for sampling from intractable target densities. The approach has been introduced in [the authors, “Exact Monte Carlo likelihood-based inference for jump-diffusion processes”, Preprint, arXiv:1707.00332] 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.

MSC:

65C50 Other computational problems in probability (MSC2010)
60J22 Computational methods in Markov chains
65C05 Monte Carlo methods
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References:

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