  The inverse temperature parameter of the Potts model governs the strength of
spatial cohesion and therefore has a major influence over the resulting model
fit. A difficulty arises from the dependence of an intractable normalising
constant on the value of this parameter and thus there is no closed-form
solution for sampling from the posterior distribution directly. There are a
variety of computational approaches for sampling from the posterior without
evaluating the normalising constant, including the exchange algorithm and
approximate Bayesian computation (ABC). A serious drawback of these algorithms
is that they do not scale well for models with a large state space, such as
images with a million or more pixels. We introduce a parametric surrogate
model, which approximates the score function using an integral curve. Our
surrogate model incorporates known properties of the likelihood, such as
heteroskedasticity and critical temperature. We demonstrate this method using
synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite.
We achieve up to a hundredfold improvement in the elapsed runtime, compared to
the exchange algorithm or ABC. An open source implementation of our algorithm
is available in the R package "bayesImageS."
