Simulation-based Bayesian machine learning methods for Cosmology and beyond

Abstract

This thesis presents a newly developed algorithm PolySwyft. This sequential simulation- based nested sampler is motivated by the limitations of likelihood-based Bayesian inference in sky-averaged 21-cm Cosmology. Moreover, PolySwyft merges nested sampling and neural ratio estimation into a general Bayesian framework, and the method is a general-purpose algorithm applicable beyond Cosmology. This thesis is divided into five sections. In the first chapter, I elaborate on the physics background of 21-cm Cosmology and its current challenges and issues on sky-averaged 21-cm parameter inference, identified as theoretical, experimental, or of statistical origin. As this thesis focuses on the data analytical aspect of sky-averaged 21-cm signal parameter inference, I introduce the fundamental principles of Bayesian inference and its algorithmic tools used in practice in chapter two. I elaborate on nested sampling and neural networks, two algorithmic methods commonly used in current cosmological inference. Moreover, I will introduce Simulation-Based Inference (SBI), an emerging statistical paradigm within Cosmology, and I will present Neural Ratio Estimation (NRE) as a method used in SBI for Cosmology. These methods are the algorithmic tools I will utilize throughout this thesis. The third chapter is on the data analysis of simulated sky-averaged 21-cm signal datasets using the REACH radio instrument. I probe artificially injected physical and statistical systematics effects on 21-cm signal parameter inference and its implications on cosmological model comparison. The fourth chapter stems from the data analytical limitations discovered in chapter three. To mitigate these statistical limitations, I apply SBI and present a novel method PolySwyft that merges nested sampling and NREs (more broadly, SBI) into a general Bayesian frame- work. I apply this new algorithm on 100 (data) times 5 (parameter) dimensional toy problems with known analytical ground truth solutions and a CMB power spectrum toy problem. Finally, in the fifth chapter, I elaborate on future research directions that this thesis and method can motivate for subsequent work.