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Simulation-based Bayesian machine learning methods for Cosmology and beyond https://doi.org/10.17863/CAM.119569 Scheutwinkel, Kilian Hikaru De Lera Acedo, Eloy Handley, Will 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. University of Cambridge 2024-10-26 Thesis Doctoral Doctor of Philosophy (PhD) Hans Werthén Foundation PhD enrichment scheme by the Alan Turing Institute PhD grant by G-Research https://www.repository.cam.ac.uk/handle/1810/386266 https://www.repository.cam.ac.uk/bitstreams/425cc84b-33a6-4226-869c-9b73aa66eb20/download ee6906deee6551d56d2749258d122ac3 https://www.repository.cam.ac.uk/bitstreams/3df61411-9ca0-4200-890e-fcb1a36ef138/download 87eda9de84448d1f82354d60eee3eb5f http://purl.org/NET/rdflicense/allrightsreserved 21-cm cosmology astrophysics bayesian data analysis bayesian inference cosmology high dimensional inference likelihood-free inference machine learning monte carlo methods nested sampling neural ratio estimation numerical methods parallel computing physics radio cosmology REACH sequential methods simulation-based inference statistical methods