Placing Constraints on Anisotropic Expansion with Type Ia Supernovae and improving Cosmological Parameter Estimation with Bayesian Hierarchical Models

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In this thesis, I aim explore the possibility of any anisotropic deviations in the rate of expansion of the universe from the currently accepted isotropic Lambda Cold Dark Matter (LCDM) cosmology as well as investigate phenomenological models that can naturally lead to such anisotropies arising. This analysis is done within the framework of the Bayesian Hierarchical Model BAHAMAS. We then look to improve the BAHAMAS framework by including the modelling of selection effects on spectroscopically classified supernovae to address the issue of Malmquist bias within supernovae datasets