Detection and Explanation of Statistical Differences Across a Pair of Groups

The task of explaining differences across groups is a task that people encounter often, not only in the research environment, but also in less formal settings.\ud Existing statistical tools designed specifically for discovering and understanding differences are limited.\ud The methods developed in this dissertation provide such tools and help understand what properties such tools should have to be successful and to motivate further development of new approaches to discovering and understanding differences.\ud \ud This dissertation presents a novel approach to comparing groups of data points.\ud The process of comparing groups of data is divided into multiple stages:\ud The learning of maximum a posteriori models for the data in each group, the identification of statistical differences between model parameters, the construction of a single model that captures those differences, and finally, the explanation of inferences of differences in marginal distributions in the form of an account of clinically significant contributions of elemental model differences to the marginal difference.\ud A general framework for the process, applicable to a broad range of model types, is presented.\ud This dissertation focuses on applying this framework to Bayesian networks over multinomial variables.\ud \ud To evaluate model learning and the detection of parameter differences an empirical evaluation of methods for identifying statistically significant differences and clinically significant differences is performed.\ud To evaluate the generated explanations of how differences in the models account for the differences in probabilities computed from those models, case studies with real clinical data are presented, and the findings generated by explanations are discussed.\ud An interactive prototype that allows a user to navigate through such an explanation is presented, and ideas are discussed for further development of data analysis tools for comparing groups of data