  Cosmological experiments often employ Bayesian workflows to derive
constraints on cosmological and astrophysical parameters from their data. It
has been shown that these constraints can be combined across different probes
such as Planck and the Dark Energy Survey and that this can be a valuable
exercise to improve our understanding of the universe and quantify tension
between multiple experiments. However, these experiments are typically plagued
by differing systematics, instrumental effects and contaminating signals, which
we collectively refer to as `nuisance' components, that have to be modelled
alongside target signals of interest. This leads to high dimensional parameter
spaces, especially when combining data sets, with > 20 dimensions of which only
around 5 correspond to key physical quantities. We present a means by which to
combine constraints from different data sets in a computationally efficient
manner by generating rapid, reusable and reliable marginal probability density
estimators, giving us access to nuisance-free likelihoods. This is possible
through the unique combination of nested sampling, which gives us access to
Bayesian evidences, and the marginal Bayesian statistics code MARGARINE. Our
method is lossless in the signal parameters, resulting in the same posterior
distributions as would be found from a full nested sampling run over all
nuisance parameters, and typically quicker than evaluating full likelihoods. We
demonstrate our approach by applying it to the combination of posteriors from
the Dark Energy Survey and Planck.
