Inverse Gaussian Process regression for likelihood-free inference

TL;DR

This paper introduces an inverse Gaussian Process regression method for likelihood-free Bayesian inference, enabling approximate posterior computation with limited simulations, demonstrating competitive performance in stability and efficiency.

Contribution

The paper proposes a novel inverse Gaussian Process regression approach for likelihood-free inference, with an adaptive algorithm and tempering to efficiently approximate marginal posteriors.

Findings

IGPR performs well in stability and efficiency

The method provides a weighted Gaussian approximation of posteriors

Competitive with existing algorithms in various examples

Abstract

In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian Process regression (IGPR), i.e., one from the output of a simulation model to the input of it. Within the method, we provide an adaptive algorithm with a tempering procedure to construct the approximations of the marginal posterior distributions. With examples we demonstrate that IGPR has a competitive performance compared to some commonly used algorithms, especially in terms of statistical stability and computational efficiency, while the price to pay is that it can only compute a weighted Gaussian approximation of the marginal posteriors.