Nested sampling with plateaus

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.

arXiv comment7 pages, 6 figures. minor changes and clarifications. closely matches published version

References in corpus (12)

• MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
• dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences
• Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
• Importance Nested Sampling and the MultiNest Algorithm
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation
• DIAMONDS: a new Bayesian Nested Sampling tool. Application to Peak Bagging of solar-like oscillations
• anesthetic: nested sampling visualisation
• Nested sampling cross-checks using order statistics
• DNest4: Diffusive Nested Sampling in C++ and Python
• Nested Sampling And Likelihood Plateaus

Cited by in corpus (12)

• Nested sampling for physical scientists
• Nested Sampling Methods
• On the detection and precise localisation of merging black holes events through strong gravitational lensing
• Strong constraints on a simple self-interacting neutrino cosmology
• Exploring phase space with Nested Sampling
• Inferring dark matter halo properties for HI-selected galaxies
• Nested sampling for frequentist computation: fast estimation of small $p$-values
• Nested Sampling And Likelihood Plateaus
• Kernel-, mean- and noise-marginalised Gaussian processes for exoplanet transits and $H_0$ inference
• Towards a Field Based Bayesian Evidence Inference from Nested Sampling Data
• Resonances in reflective Hamiltonian Monte Carlo
• FreeBird.jl: An Extensible Toolbox for Simulating Interfacial Phase Equilibria