  Most of the existing algorithms for approximate Bayesian computation (ABC)
assume that it is feasible to simulate pseudo-data from the model at each
iteration. However, the computational cost of these simulations can be
prohibitive for high dimensional data. An important example is the Potts model,
which is commonly used in image analysis. Images encountered in real world
applications can have millions of pixels, therefore scalability is a major
concern. We apply ABC with a synthetic likelihood to the hidden Potts model
with additive Gaussian noise. Using a pre-processing step, we fit a binding
function to model the relationship between the model parameters and the
synthetic likelihood parameters. Our numerical experiments demonstrate that the
precomputed binding function dramatically improves the scalability of ABC,
reducing the average runtime required for model fitting from 71 hours to only 7
minutes. We also illustrate the method by estimating the smoothing parameter
for remotely sensed satellite imagery. Without precomputation, Bayesian
inference is impractical for datasets of that scale.
