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.

翻译：贝叶斯分析已成为宇宙学多个领域不可或缺的工具，涵盖引力波研究、宇宙微波背景辐射以及宇宙黎明时期的21厘米信号等现象。该方法可对描述关键宇宙学与天体物理信号的复杂模型进行拟合，同时处理大量污染信号及仪器效应（以“ nuisance参数”建模）。本文总结了一种利用掩码自回归流与核密度估计学习核心科学参数边际后验密度的方法。我们发现，经边际化处理（即去除 nuisance参数）的后验及其关联似然函数具有广泛的应用场景，包括：计算先前难以处理的边际库尔贝格-莱布勒散度与边际贝叶斯模型维度、似然函数仿真以及先验分布仿真。我们通过玩具模型、21厘米宇宙学实例以及暗能量巡天数据对每项应用进行了演示。讨论如何利用边际汇总统计量（如库尔贝格-莱布勒散度与贝叶斯模型维度）评估不同实验的约束能力，以及如何借助边际先验与似然仿真器实现高效联合分析。我们将多用途代码封装为可通过pip安装的margarine工具包，供科学界广泛使用。