Nested sampling with any prior you like. (arXiv:2102.12478v1 [astro-ph.IM])

Nested sampling with any prior you like. (arXiv:2102.12478v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Alsing_J/0/1/0/all/0/1">Justin Alsing</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Handley_W/0/1/0/all/0/1">Will Handley</a>

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 that prior distributions be provided in the form of
bijective 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.

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 that prior distributions be provided in the form of
bijective 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.

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