Nested sampling cross-checks using order statistics

TL;DR

This paper introduces a new cross-check method for nested sampling based on order statistics, which detects failures and unreliable results in NS runs across various applications and dimensions.

Contribution

The authors identify a novel property of nested sampling related to order statistics and develop a simple, effective cross-check method for validating NS results.

Findings

The cross-check detects failures in NS sampling.

It works across different likelihoods and dimensions.

It is recommended as a standard validation step.

Abstract

Nested sampling (NS) is an invaluable tool in data analysis in modern astrophysics, cosmology, gravitational wave astronomy and particle physics. We identify a previously unused property of NS related to order statistics: the insertion indexes of new live points into the existing live points should be uniformly distributed. This observation enabled us to create a novel cross-check of single NS runs. The tests can detect when an NS run failed to sample new live points from the constrained prior and plateaus in the likelihood function, which break an assumption of NS and thus leads to unreliable results. We applied our cross-check to NS runs on toy functions with known analytic results in 2 - 50 dimensions, showing that our approach can detect problematic runs on a variety of likelihoods, settings and dimensions. As an example of a realistic application, we cross-checked NS runs performed in the context of cosmological model selection. Since the cross-check is simple, we recommend that it become a mandatory test for every applicable NS run.