Non-linear regression models for Approximate Bayesian Computation

TL;DR

This paper introduces a novel machine-learning approach for Approximate Bayesian Computation that employs non-linear regression and importance sampling to improve efficiency and reduce computational costs in complex inference problems.

Contribution

It proposes a new nonlinear regression-based method with adaptive importance sampling for more efficient Bayesian inference with summary statistics.

Findings

Significantly reduces computational burden in genetic and queueing models

Outperforms existing ABC methods in accuracy and efficiency

Demonstrates effectiveness on real-world complex inference problems

Abstract

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.