Hierarchical inference of evidence using posterior samples

TL;DR

This paper introduces a hierarchical method to estimate Bayesian evidence efficiently by leveraging posterior samples and a multivariate normal approximation, improving model selection processes.

Contribution

The paper presents a novel hierarchical approach that uses posterior samples and a multivariate normal approximation to infer Bayesian evidence more effectively.

Findings

Enables evidence estimation from arbitrary posterior samples

Uses a hierarchical framework for improved accuracy

Applicable to various sampling schemes

Abstract

The Bayesian evidence, crucial ingredient for model selection, is arguably the most important quantity in Bayesian data analysis: at the same time, however, it is also one of the most difficult to compute. In this paper we present a hierarchical method that leverages on a multivariate normalised approximant for the posterior probability density to infer the evidence for a model in a hierarchical fashion using a set of posterior samples drawn using an arbitrary sampling scheme.