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Bayesian analysis has become an indispensable tool across many differentcosmological fields including the study of gravitational waves, the CosmicMicrowave Background and the 21-cm signal from the Cosmic Dawn among otherphenomena. The method provides a way to fit complex models to data describingkey cosmological and astrophysical signals and a whole host of contaminatingsignals and instrumental effects modelled with `nuisance parameters'. In thispaper, we summarise a method that uses Masked Autoregressive Flows and KernelDensity Estimators to learn marginal posterior densities corresponding to corescience parameters. We find that the marginal or 'nuisance-free' posteriors andthe associated likelihoods have an abundance of applications including; thecalculation of previously intractable marginal Kullback-Leibler divergences andmarginal Bayesian Model Dimensionalities, likelihood emulation and prioremulation. We demonstrate each application using toy examples, examples fromthe field of 21-cm cosmology and samples from the Dark Energy Survey. Wediscuss how marginal summary statistics like the Kullback-Leibler divergencesand Bayesian Model Dimensionalities can be used to examine the constrainingpower of different experiments and how we can perform efficient joint analysisby taking advantage of marginal prior and likelihood emulators. We package ourmultipurpose code up in the pip-installable code margarine for use in the widerscientific community.

Marginal Post Processing of Bayesian Inference Products with Normalizing Flows and Kernel Density Estimators