Collecting and interpreting data is key to developing an understanding of the physical underpinnings of observable events. As such, questions of how to generate, curate and otherwise wrangle data become central as systems of interest become increasingly difficult to access experimentally and the sheer quantity of raw information explodes. The data explored in this dissertation covers a wide range of sources and methods. On the more traditional end, we explore simulation data of the two dimensional non-equilibrium random-field Ising model which we treat with a novel analytic normal form theory of the Renormalization Group. Branching out from condensed matter, we explore several machine learning and sampling methods in various contexts. The machine learning projects in particular include three lines of investigation: an unsupervised machine learning analysis of sectors of the economy extracted from stock return data, an analysis of the computational neural networks successfully applied to experimental ATLAS data in a recent Kaggle challenge, and an exploration of the geometrical underpinnings of canonical neural networks using a Jeffrey’s Prior sampling of trained networks.