Data-Driven Analyses of Supersymmetric Models and Their Cosmological and Phenomenological Consequences

With such a rich plethora of models to explain the mysteries of modern theoretical physics, the role of phenomenology is critical in ascertaining the viability of said models against experimental result. Furthermore, as the ambition and scope of these models grows, sophisticated data science techniques are more relevant than ever in handling such models. In this thesis, I present the work I have done in applying data techniques to extensions of supersymmetric models which remains one of the most attractive candidates for physics beyond the Standard Model. In particular, I present the results of my work developing and applying algorithmic frameworks for analysing high scale parameters of these models and linking phenomenological tools in order to analyse various experimental results of these models. In essence, the models presented display two different approaches to the fine-tuning problems in supersymmetry where in one we fix parameters to be natural, and in the second we allow for non-minimal-flavour-violation. In this manuscript, I first briefly introduce the Standard Model and its shortcomings as well as supersymmetric extensions to the Standard Model and some alternative approaches to beyond the Standard Model physics. I then show the results of a no-scale supergravity model where the universal scalar mass is zero. We have a particular focus on the recent muon g-2 experimental results as well as dark matter and the Higgs boson mass. These models naturally arise from string theory and are also inspired by Starobinsky inflation which places further phenomenological constraints on the model. We find that certain regions of parameter space can satisfy these constraints with requisite light sleptons close to the LHC excluded region. I also display the work I did in implementing a Markhov chain MonteCarlo scan of a supersymmetric grand unified theory of flavour. In this analysis, a huge number of phenomenological constraints were applied to examine the allowed flavour structure. The model naturally predicted large sleptonic mixing explaining their LHC evation and light winos and gluinos suggesting the good prospect for discovering these particles in up-coming collider runs. This thesis contains work based on two preprint publications with arXiv numbers arXiv:2111.10199, and arXiv:2111.10199.