Nested sampling cross-checks using order statistics

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.

minor changes & clarifications. closely matches published version

References in corpus (34)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• 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
• Tests of general relativity with GW150914
• Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
• X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue
• Binary Black Hole Mergers in the first Advanced LIGO Observing Run
• Bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy
• Information criteria for astrophysical model selection
• Importance Nested Sampling and the MultiNest Algorithm
• Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library
• Conservative Constraints on Early Cosmology: an illustration of the Monte Python cosmological parameter inference code
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• A search for ultra-light axions using precision cosmological data
• Curvature tension: evidence for a closed universe
• A Nested Sampling Algorithm for Cosmological Model Selection
• Constraints on cosmic-ray propagation models from a global Bayesian analysis
• The Best Inflationary Models After Planck
• A statistical test for Nested Sampling algorithms
• Model selection and parameter inference in phylogenetics using Nested Sampling
• The impact of priors and observables on parameter inferences in the Constrained MSSM
• Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating
• Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results
• The CMSSM and NUHM1 after LHC Run 1
• anesthetic: nested sampling visualisation
• Determining pressure-temperature phase diagrams of materials
• Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module
• Sampling Errors in Nested Sampling Parameter Estimation
• nestcheck: diagnostic tests for nested sampling calculations
• Constant-pressure nested sampling with atomistic dynamics
• Superposition Enhanced Nested Sampling
• Initializing adaptive importance sampling with Markov chains
• Nested Sampling And Likelihood Plateaus

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