Nested sampling with plateaus

TL;DR

This paper introduces a simple modification to nested sampling that effectively handles likelihood plateaus, improving the accuracy of evidence and posterior estimates, and can be applied retrospectively to existing runs.

Contribution

A novel, straightforward modification to nested sampling that manages plateaus by evicting live points individually, applicable to existing NS implementations.

Findings

Improved evidence estimates on plateau problems

Retrospective application to existing NS runs

Proposed as the canonical version of NS

Abstract

It was recently emphasised by Riley (2019); Schittenhelm & Wacker (2020) that that in the presence of plateaus in the likelihood function nested sampling (NS) produces faulty estimates of the evidence and posterior densities. After informally explaining the cause of the problem, we present a modified version of NS that handles plateaus and can be applied retrospectively to NS runs from popular NS software using anesthetic. In the modified NS, live points in a plateau are evicted one by one without replacement, with ordinary NS compression of the prior volume after each eviction but taking into account the dynamic number of live points. The live points are replenished once all points in the plateau are removed. We demonstrate it on a number of examples. Since the modification is simple, we propose that it becomes the canonical version of Skilling's NS algorithm.