Barker's algorithm for Bayesian inference with intractable likelihoods

TL;DR

This paper presents a simple MCMC scheme based on Barker's algorithm and a Bernoulli factory for Bayesian inference with intractable likelihoods, offering an alternative to traditional methods.

Contribution

It introduces a Barker's algorithm-based MCMC method with a Bernoulli factory, enabling Bayesian inference without extended state spaces in intractable likelihood scenarios.

Findings

Applicable to jump-diffusions and Wright-Fisher diffusions

Allows implementation of marginal Barker's algorithm

Provides an alternative to pseudo-marginal methods

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 Gon\c{c}alves 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.