What does a cosmological experiment really measure? Covariant posterior decomposition with normalizing flows

TL;DR

This paper introduces non-linear, machine-learning-based methods using normalizing flows to extract and decompose constrained parameter combinations from complex, non-Gaussian posterior distributions in cosmological data analysis.

Contribution

It develops a novel non-linear posterior decomposition technique that is basis-independent and applicable to non-Gaussian distributions, advancing cosmological parameter inference.

Findings

Successfully applied to DES and Planck data posteriors

Automatically identifies survey-specific constrained parameters like S8

Estimates H0 from large-structure data alone

Abstract

We present methods to rigorously extract parameter combinations that are constrained by data from posterior distributions. The standard approach uses linear methods that apply to Gaussian distributions. We show the limitations of the linear methods for current surveys, and develop non-linear methods that can be used with non-Gaussian distributions, and are independent of the parameter basis. These are made possible by the use of machine-learning models, normalizing flows, to learn posterior distributions from their samples. These models allow us to obtain the local covariance of the posterior at all positions in parameter space and use its inverse, the Fisher matrix, as a local metric over parameter space. The posterior distribution can then be non-linearly decomposed into the leading constrained parameter combinations via parallel transport in the metric space. We test our methods on two non-Gaussian, benchmark examples, and then apply them to the parameter posteriors of the Dark Energy Survey and Planck CMB lensing. We illustrate how our method automatically learns the survey-specific, best constrained effective amplitude parameter $S_8$ for cosmic shear alone, cosmic shear and galaxy clustering, and CMB lensing. We also identify constrained parameter combinations in the full parameter space, and as an application we estimate the Hubble constant, $H_0$, from large-structure data alone.