Bayesian evaluation of informative hypotheses

Abstract

The evaluation of informative hypotheses has gained in popularity in applied sciences, because it enables researchers to investigate their expectations with respect to the population of interest. In this dissertation, approximate Bayesian approaches are developed to evaluate informative hypotheses by means of the Bayes factor in a very general class of statistical models. The Bayes factor quantifies the support from the data in favor of one hypothesis against another. The computation of the Bayes factor requires the specification of the prior distribution and the derivation of the posterior distribution for model parameters under the unconstrained hypothesis. This dissertation proposes default prior specification methods and normally approxiamtes the posterior distribution. Two software packages are developed for the computation of the Bayes factor.