Nested sampling with any prior you like

Abstract

Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing marginal likelihoods for model comparison. One technical obstacle to using nested sampling in practice is the requirement (for most common implementations) that prior distributions be provided in the form of transformations from the unit hyper-cube to the target prior density. For many applications - particularly when using the posterior from one experiment as the prior for another - such a transformation is not readily available. In this letter we show that parametric bijectors trained on samples from a desired prior density provide a general-purpose method for constructing transformations from the uniform base density to a target prior, enabling the practical use of nested sampling under arbitrary priors. We demonstrate the use of trained bijectors in conjunction with nested sampling on a number of examples from cosmology.

arXiv comment5 pages, 2 figures, Published as an MNRAS letter

References in corpus (18)

• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
• The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Tensions between the Early and the Late Universe
• Planck 2018 results. V. CMB power spectra and likelihoods
• Planck evidence for a closed Universe and a possible crisis for cosmology
• New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• Curvature tension: evidence for a closed universe
• The evidence for a spatially flat Universe
• Masked Autoregressive Flow for Density Estimation
• Nested Sampling with Normalising Flows for Gravitational-Wave Inference
• anesthetic: nested sampling visualisation
• nestcheck: diagnostic tests for nested sampling calculations
• Accelerated Bayesian inference using deep learning
• The Standard Model of Cosmology: A Skeptic's Guide

Cited by in corpus (12)

• Nested sampling for physical scientists
• Importance nested sampling with normalising flows
• Bayesian Stokes inversion with Normalizing flows
• Spectroastrometry and Reverberation Mapping: the Mass and Geometric Distance of the Supermassive Black Hole in the Quasar 3C 273
• Analytical marginalisation over photometric redshift uncertainties in cosmic shear analyses
• A Stimulating Explanation of the Extragalactic Radio Background
• The effect of spin mismodeling on gravitational-wave measurements of the binary neutron star mass distribution
• The impact of the Universe's expansion rate on constraints on modified growth of structure
• Bayesian evidence-driven diagnosis of instrumental systematics for sky-averaged 21-cm cosmology experiments
• Exploring phase space with Nested Sampling
• Gaussian discriminators between $\Lambda$CDM and wCDM cosmologies using expansion data
• APES: Approximate Posterior Ensemble Sampler