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Bayesian Hypothesis Testing And Variable Selection In High Dimensional Regression, Min Wang

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This dissertation consists of three distinct but related research projects. First of all, we study the Bayesian approach to model selection in the class of normal regression models. We propose an explicit closed-form expression of the Bayes factor with the use of Zellner's g-prior and the beta-prime prior for g. Noting that linear models with a growing number of unknown parameters have recently gained increasing popularity in practice, such as the spline problem, we shall thus be particularly interested in studying the model selection consistency of the Bayes factor under the scenario in which the dimension of the parameter space …