On statistical uncertainty in nested sampling

TL;DR

This paper investigates the statistical uncertainty in Bayesian evidence computed via nested sampling, comparing existing and new estimators, both of which accurately quantify uncertainty without extra computational effort.

Contribution

It introduces a new estimator for the statistical uncertainty in nested sampling evidence, enhancing accuracy and efficiency over previous methods.

Findings

Both estimators perform well in test cases.

The new estimator provides reliable uncertainty estimates.

Uncertainty can be obtained without additional computational cost.

Abstract

Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the parameter space. I study the statistical uncertainty in the evidence computed with nested sampling. I examine the uncertainty estimator from Skilling (2004, 2006) and introduce a new estimator based on a detailed analysis of the statistical properties of nested sampling. Both perform well in test cases and make it possible to obtain the statistical uncertainty in the evidence with no additional computational cost.