Towards a Field Based Bayesian Evidence Inference from Nested Sampling Data

TL;DR

This paper introduces a Bayesian inference approach to improve the accuracy of nested sampling for computing Bayesian evidence, especially with limited samples, by modeling likelihood-prior volume relations as a smooth function.

Contribution

It transforms prior volume estimation into a Bayesian inference problem, enhancing nested sampling accuracy through a post-processing method that models likelihood-prior volume relations.

Findings

Significant accuracy improvement with fewer than 100 active samples.

Method works as a post-processing step for nested sampling.

Prone to numerical issues with larger sample sizes.

Abstract

Nested sampling (NS) is a stochastic method for computing the log-evidence of a Bayesian problem. It relies on stochastic estimates of prior volumes enclosed by likelihood contours, which limits the accuracy of the log-evidence calculation. We propose to transform the prior volume estimation into a Bayesian inference problem, which allows us to incorporate a smoothness assumption for likelihood-prior volume relations. As a result, we aim to increase the accuracy of the volume estimates and thus improve the overall log-evidence calculation using NS. The method presented works as a post-processing step for NS and provides posterior samples of the likelihood-prior-volume relation, from which the log-evidence can be calculated. We demonstrate an implementation of the algorithm and compare its results with plain NS on two synthetic datasets for which the underlying evidence is known. We find a significant improvement in accuracy for runs with less than one hundred active samples in NS, but are prone to numerical problems beyond this point.