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Hierarchical Bayesian Models for Investigating Astrophysical Systematics in Type Ia Supernova Cosmology https://doi.org/10.17863/CAM.114148 Ward, Sam Dhawan, Suhail Mandel, Kaisey Type Ia supernovae (SNe Ia) are stellar explosions, and standardisable candles, used to estimate luminosity distances and constrain cosmological parameters. With increasing SN Ia sample sizes (≳ 1000 objects), systematic uncertainties in SN distance estimates now dominate inferences in SN cosmology. The goal then is to improve SN Ia standardisation to enhance their utility as cosmological probes. To do this, the astrophysics that drives observed correlations between SN brightnesses, and their host galaxy properties, must be understood. I review state-of-the-art studies of SN-host correlations in Chapter 1, which specifically motivate the work in this thesis, and discuss statistical methods such as hierarchical Bayesian modelling and Gaussian processes in Chapter 2, which are used extensively throughout. In the subsequent Chapters, I explore two distinct avenues for better understanding empirical SN-host correlations. The first involves the development of new hierarchical Bayesian methods for rapidly inferring SN-host dust population distributions from SN brightness measurements, without assuming any cosmology (Chapter 3). The second similarly involves the development of various forward models for ‘SN siblings’: SNe that exploded in the same host galaxy (Chapters 4, 5). This thesis thus contributes multiple fundamental conceptual developments for SN Ia modelling, including: the intrinsic deviations formalism for cosmology-independent hierarchical modelling of chromatic brightness measurements, censored-data modelling for building a cosmological sample of SNe Ia that is consistent with the forward model, and the relative intrinsic scatter hyperparameter, 𝜎Rel, for hierarchically modelling and analysing siblings. Further developing and applying these models to future larger samples of SNe Ia may lead to improvements in SN Ia standardisation for cosmology. In Chapter 3, I build the publicly-available Bird-Snack model, to perform Bayesian Inference of R𝑉 Distributions using SN Ia Apparent Colours at peaK. I use Gaussian processes and a hierarchical Bayesian model to analyse optical-to-near-infrared light curves of 65 low-redshift SNe Ia with data near peak-brightness, and infer the host galaxy dust population distributions without assuming any cosmology. I identify new best practices and avenues of research for future hierarchical Bayesian analyses of larger samples. In Chapter 4, I develop and model 𝜎Rel – the intrinsic scatter of siblings photometric distance estimates relative to one another within a galaxy – to analyse a unique system of three SN Ia siblings in the nearby Cepheid-calibrator galaxy, NGC 3147. Their photometric data include new Pan-STARRS-1 𝑔𝑟𝑖𝑧𝑦 light curves of the new sibling, SN 2021hpr, from the Young Supernova Experiment. I develop a bespoke model that facilitates, for the first time, a simultaneous fit to the siblings’ light curves, whilst marginalising over 𝜎Rel with an informative hyperprior; this demonstrates how siblings can be robustly modelled to study SN-host correlations. I then apply this model to infer the Hubble constant, further demonstrating how siblings can be hierarchically modelled to infer cosmology. In Chapter 5, I develop new publicly available methods to hierarchically analyse the spectroscopic sample of 12 SN Ia sibling-pair galaxies from the Zwicky Transient Facility survey. I use simulations to investigate the efficacy of various hyperprior choices for constraining the siblings’ intrinsic scatter hyperparameters, and, for the first time, place constraints on the correlation between photometric distance estimates to SN Ia siblings. In Chapter 6, I summarise this thesis’ outcomes and present an outlook for future work. University of Cambridge 2024-08-30 Thesis Doctoral Doctor of Philosophy (PhD) eng https://www.repository.cam.ac.uk/handle/1810/377285 https://www.repository.cam.ac.uk/bitstreams/2081b957-8246-435c-b7ae-4e6477ba5b55/download a817e14c1b92aa52bb41081cfffaf55c https://www.repository.cam.ac.uk/bitstreams/ea4c51f3-3837-46d6-a0b0-270017e4fd98/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ Astronomy Astrostatistics Cosmology Hierarchical Bayes Supernovae