Improving the efficiency and robustness of nested sampling using posterior repartitioning

TL;DR

This paper introduces a posterior repartitioning method for nested sampling that improves efficiency and robustness by reconfiguring the likelihood and prior without altering the posterior or evidence, especially when priors are unrepresentative.

Contribution

The novel posterior repartitioning method enhances nested sampling efficiency by redefining likelihood and prior while preserving their product, addressing unrepresentative priors in Bayesian inference.

Findings

Significant increase in sampling efficiency with PR method

Maintains accurate posterior and evidence estimates

Effective for unrepresentative prior scenarios

Abstract

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings of the assumed prior distribution, this can lead to extremely inefficient exploration of the resulting posterior by nested sampling algorithms, with unnecessarily high associated computational costs. Simple solutions such as broadening the prior range in such cases might not be appropriate or possible in real-world applications, for example when one wishes to assume a single standardised prior across the analysis of a large number of datasets for which the true values of the parameters of interest may vary. This work therefore introduces a posterior repartitioning (PR) method for nested sampling algorithms, which addresses the problem by redefining the likelihood and prior while keeping their product fixed, so that the posterior inferences and evidence estimates remain unchanged but the efficiency of the nested sampling process is significantly increased. Numerical results show that the PR method provides a simple yet powerful refinement for nested sampling algorithms to address the issue of unrepresentative priors.