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Bayesian analysis has become an indispensable tool across many different
cosmological fields including the study of gravitational waves, the Cosmic
Microwave Background and the 21-cm signal from the Cosmic Dawn among other
phenomena. The method provides a way to fit complex models to data describing
key cosmological and astrophysical signals and a whole host of contaminating
signals and instrumental effects modelled with 'nuisance parameters'. In this
paper, we summarise a method that uses Masked Autoregressive Flows and Kernel
Density Estimators to learn marginal posterior densities corresponding to core
science parameters. We find that the marginal or 'nuisance-free' posteriors and
the associated likelihoods have an abundance of applications including; the
calculation of previously intractable marginal Kullback-Leibler divergences and
marginal Bayesian Model Dimensionalities, likelihood emulation and prior
emulation. We demonstrate each application using toy examples, examples from
the field of 21-cm cosmology and samples from the Dark Energy Survey. We
discuss how marginal summary statistics like the Kullback-Leibler divergences
and Bayesian Model Dimensionalities can be used to examine the constraining
power of different experiments and how we can perform efficient joint analysis
by taking advantage of marginal prior and likelihood emulators. We package our
multipurpose code up in the pip-installable code margarine for use in the wider
scientific community.
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