Nested sampling with any prior you like
  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.
