STATISTICAL LEARNING FOR STANDARD MODEL PHENOMENOLOGY

The focus of this thesis is the accurate determination of parton distribution functions (PDFs), with a particular emphasis on modern machine learning tools used within the NNPDF approach. We first present NNPDF4.0, currently the most recent and most precise set of PDFs based on a global dataset. We then provide suggestions for improvements to the machine learning tools used for the NNPDF4.0 determination, both in terms of parametrization and model selection. We discuss different sources of PDF uncertainty. First, we elucidate the nontrivial aspects of averaging over the space of PDF determinations by explicitly calculating the data-driven correlation between different sets of PDFs. Then, we lay out certain fundamental properties of the sampling as performed within NNPDF methodology through explicit examples, and discuss how one may gain insight into the results of a neural network fit despite it being a black box model. Finally, we show how the flexibility of the NNPDF methodology allows for it to be applied to problems other than PDF determination, in particular we present a determination of neutrino inelastic structure functions.