Nested sampling with any prior you like

TL;DR

This paper introduces a method using trained parametric bijectors to enable nested sampling with arbitrary priors, overcoming a key technical obstacle and broadening its practical applicability in Bayesian analysis.

Contribution

It proposes a general approach to construct prior transformations using trained bijectors, allowing nested sampling with any prior distribution without explicit transformations.

Findings

Successfully applied to cosmological examples

Enables nested sampling with arbitrary priors

Overcomes limitations of existing implementations

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.