  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.
