Contributions to Bayesian Statistical Modeling in Public Policy Research

Abstract

This dissertation improves existing Bayesian statistical methodologies and applies these improvements to a variety of important public policy questions. The manuscript is divided into six chapters. The first chapter provides an overview of the various chapters of the dissertation. The second chapter improves existing Bayesian binary logistic regression methodologies using polynomial expansions as an alternative to existing Markov Chain Monte Carlo (MCMC) methods. Our improvements make the estimation technique quite useful for a variety of applications. We also demonstrate the methodology to be considerably faster than existing MCMC methods. These computational gains are quite useful for models analyzing large data sets involving high-dimensional parameter spaces. We apply this methodology to a child poverty data set to analyze the potential causes of child poverty. The next chapter improves upon a well-known technique in semiparametric modeling known as density ratio estimation. This methodology is useful in principle; however, it suffers from one primary limitation - The technique has thus far been incapable of modeling individual-level heterogeneity. Modeling heterogeneity is important as there is often no a priori reason to believe that different individuals (or observations) in a data set will behave in an identical manner. We ameliorate this limitation in the third chapter of this dissertation by adapting density ratio estimation methods to accommodate individual-level heterogeneity. We apply this new methodology to an analysis of the efficacy of medical malpractice reform across the country. In the fourth chapter of this dissertation, we shift our focus toward improving Bayesian credible interval estimation via semiparametric density ratio estimation. We do so by applying an innovative adaptation of the methodology, known as out of sample fusion, to posterior samples from a hierarchical Bayesian linear model looking at the efficacy of the welfare reform of the 1990s. In the fifth chapter, we extend the application of this methodology to credible interval estimation of a hierarchical generalized linear model used for analyzing terrorism data in a number of major conflicts across the globe. We use our results to offer some prescriptive policy suggestions regarding counterterrorism policy. The final chapter concludes the dissertation and offers a number of suggestions for further research. We emphasize that the modeling contributions presented in this dissertation are useful in myriads of other applied problems beyond just the public policy applications presented here.