GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

TL;DR

This paper introduces GPS-ABC, a novel Gaussian process surrogate method for Approximate Bayesian Computation that reduces the number of simulations needed for posterior inference in complex models.

Contribution

The paper presents two new ABC algorithms that adaptively determine the number of simulations using confidence estimates, improving efficiency over traditional methods.

Findings

Significantly fewer simulations required for accurate posterior inference.

Effective surrogate modeling with Gaussian processes for complex biological problems.

Demonstrated success on realistic biological case studies.

Abstract

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. 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 posterior inference. Both algorithms use confidence estimates for the accept probability in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from every 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.