Thomas, AnthonyWhite, MartinHunt-Smith, Nicholas Timothy2025-06-132025-06-132025https://hdl.handle.net/2440/145192In the Standard Model (SM) of particle physics, the strong force stands as one of the central components that help us interpret our world down to the smallest scale. However, the theoretical framework of Quantum Chromodynamics (QCD) which governs the strong force is made significantly more difficult to apply as one reduces the energy of the particles involved. At this energy scale we can no longer operate entirely within the basic perturbative theory that we understand very well. One way of dealing with these non-perturbative effects inherent to many QCD interactions is to make use of global QCD analysis, whereby we take as much experimental particle collision data as we can and feed it into a model containing parton distribution functions (PDFs), which describe the makeup of various composite particles. In this thesis we will investigate many different approaches to global QCD analysis, comparing how each method performs for various toy problems as well as realistic fits. We will develop new ways of improving the efficiency of such algorithms before testing them against one another. We will also perform multiple state-of-the-art global analyses. aiming to further constrain spin-dependent PDFs including new data at high-x as well as from lattice QCD. We will operate beyond the confines of the SM to search for potential dark matter candidates, placing limits on dark boson models using our knowledge of fundamental physics from global QCD analysis. In discussing these various topics, we will demonstrate the central role QCD has in many different fields within particle physics, as well as the necessity of sophisticated algorithmic approaches in order to further our understanding of hadronic structure.enParton DistributionsDark MatterBayesian samplingQuantum ChromodynamicsThesis