Essays on Bayesian Methods and Machine Learning Applied to Political Science

This dissertation presents three papers on Bayesian methods and machine learning applied to research questions in political science. The papers are unified by creating new methods that extend research from other disciplines to target specific substantive questions faced by social scientists. The first paper is focused on "Bayesian structured sparsity.'' This method relies on approaches that extend traditional sparse methods (such as the LASSO) to cluster or group parameters together while allowing researchers to explicitly integrate their prior beliefs about group-formation. I apply it to estimating heterogeneous effects, and I derive novel results about a Bayesian formulation of this method. The second paper outlines "marginally augmented variational Bayes.'' It develops a novel algorithm for estimating non-linear hierarchical models with variational inference. It then outlines a procedure for post-processing and improving the approximation using parameter expansion. Taken together, this allows hierarchical models to be scaled to large and complex problems at limited computational cost. The third paper outlines a framework for estimating ideal points when the observed data are multinomial (i.e. more than two responses). These methods are applied to a variety of questions in political science including, respectively, a re-examination of an experiment about legislative credit-claiming, estimating a model of voter turnout for demographic and state sub-groups, and understanding non-response in the American National Election Study.