  Inference for doubly intractable distributions is challenging because the
intractable normalizing functions of these models include parameters of
interest. Previous auxiliary variable MCMC algorithms are infeasible for
multi-dimensional models with large data sets because they depend on expensive
auxiliary variable simulation at each iteration. We develop a fast Bayesian
indirect algorithm by replacing an expensive auxiliary variable simulation from
a probability model with a computationally cheap simulation from a surrogate
model. We learn the relationship between the surrogate model parameters and the
probability model parameters using Gaussian process approximations. We apply
our methods to challenging simulated and real data examples, and illustrate
that the algorithm addresses both computational and inferential challenges for
doubly intractable distributions. Especially for a large social network model
with 10 parameters, we show that our method can reduce computing time from
about 2 weeks to 5 hours, compared to the previous method. Our method allows
practitioners to carry out Bayesian inference for more complex models with
larger data sets than before.
