We consider Bayesian inference problems with computationally intensive
likelihood functions. We propose a Gaussian process (GP) based method to
approximate the joint distribution of the unknown parameters and the data...
particular, we write the joint density approximately as a product of an
approximate posterior density and an exponentiated GP surrogate. We then
provide an adaptive algorithm to construct such an approximation, where an
active learning method is used to choose the design points. With numerical
examples, we illustrate that the proposed method has competitive performance
against existing approaches for Bayesian computation.