Nested sampling with any prior you like
This solves a technical obstacle for researchers in fields like astronomy who need to use nested sampling with complex or derived priors, making Bayesian analysis more accessible.
The paper tackles the problem of using nested sampling with arbitrary prior distributions by introducing a method that trains parametric bijectors on samples from a desired prior, enabling transformations from a uniform base density to any target prior. They demonstrate this approach on cosmological examples, showing it works in practice.
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.