GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

Abstract

Scientists often express their understanding of the world through a computation-ally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challeng-ing. The Approximate Bayesian Computation (ABC) framework is the standard statistical tool to handle these likelihood free problems, but they require a very large number of simulations. In this work we develop two new ABC sampling algorithms that significantly reduce the number of simulations necessary for pos-terior inference. Both algorithms use confidence estimates for the accept probabil-ity in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from ev-ery simulation in a Gaussian process which acts as a surrogate function for the simulated statistics. Experiments on a challenging realistic biological problem illustrate the potential of these algorithms. 1