Observation of the hypothetical neutrinoless double beta decay (0νββ) would prove that the neutrino is Majorana in nature, while a measurement of the half-life of the interaction could determine the absolute mass scale of neutrinos. This work presents advancements that have been made in three research campaigns that are intended to improve two 0νββ experiments - nEXO and its prototype EXO-200. First, a method for predicting breakdown voltages in dielectrics through pattern recognition is applied to a liquid xenon time projection chamber. A proposed extension to this method, which aims to incorporate the statistical variations of breakdown in liquid dielectrics, is outlined. Advancements in applying machine learning ensemble methods to event discrimination in EXO-200 are presented, along with the basics of a new formalism for applying statistical inference to all classification algorithms. Finally, simulations of two barium-tagging concepts for nEXO are summarized.