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Bayesian Variable Selection And Post-Selection Inference, Qiyiwen Zhang

Arts & Sciences Electronic Theses and Dissertations

In this dissertation, we first develop a novel perspective to compare Bayesian variable selection procedures in terms of their selection criteria as well as their finite-sample properties. Secondly, we investigate Bayesian post-selection inference in two types of selection problems: linear regression and population selection. We will demonstrate that both inference problems are susceptible to selection effects since the selection procedure is data-dependent. Before comparing Bayesian variable selection procedures, we first classify the current Bayesian variable selection procedures into two classes: those with selection criteria defined on the space of candidate models, and those with selection criteria not explicitly formulated on …