Efficient Bernoulli factory MCMC for intractable likelihoods
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Accept-reject based Markov chain Monte Carlo (MCMC) algorithms have traditionally utilised an acceptance function that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is rendered almost useless in Bayesian MCMC problems with intractable likelihoods. We introduce a new MCMC acceptance probability that has the distinguishing feature of not being a function of the ratio of the target density at the two points. We present an efficient and stable Bernoulli factory that generates events of this acceptance probability. The resulting portkey Barker's algorithm is exact and computationally more efficient that the current state-of-the-art.
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