Adaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions

TL;DR

This paper introduces an adaptive Gaussian process-based method to efficiently approximate Bayesian inference when likelihood functions are computationally expensive, using active learning to select informative points.

Contribution

It presents a novel adaptive GP approximation framework that combines surrogate modeling with active learning for efficient Bayesian inference with costly likelihoods.

Findings

Competitive performance against existing Bayesian computation methods

Effective active learning strategy for selecting design points

Accurate approximation of joint posterior distribution

Abstract

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. In 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.