Predictive Alternatives in Bayesian Model Selection

Predictive Alternatives in Bayesian Model Selection by Womack, Andrew Doctor of Philosophy in Mathematics, Washington University in St. Louis, May, 2011. Professor Jeff Gill, Chairperson Model comparison and hypothesis testing is an integral part of all data analyses. In this thesis, I present two new families of information criteria that can be used to perform model comparison. In Chapter 1, I review the necessary background to motivate the thesis. Of particular interest is the role of priors for estimation and model comparison as well as the role that information theory can play in the latter. As we will see, many existing forms of model comparison can be viewed in an information theoretic manner, which motivates defining new families of criteria. In Chapter 2, I present the two new criteria and discuss their properties. The first criterion is based purely on posterior predictive densities and Kullback-Leibler divergences and decomposes into terms that describe the fit and complexity of the model. In this manner, it behaves similar to popular criteria, such as the AIC or the DIC. I then present