Objective priors under the alpha-divergence measures

Abstract

Without prior knowledge, objective priors are derived from an assumed model for Bayesian inference. A popular approach is to elicit an objective prior which asymptotically maximizes the expected divergence measure between a prior and its corresponding posterior. The class of α-divergence measures has been used for unified prior selection recently as this class includes many widely used divergence measures. However, there is a lack of rigorous derivation of objective priors in the presence of nuisance parameters under the α-divergence measure. Neglecting nuisance parameters may lead to unsatisfactory objective Bayesian inference. In this thesis, a rigorous method is developed to elicit objective priors in the presence of nuisance parameters using the α-divergence measure. This new class of objective priors is called alpha priors. Alpha priors with independence assumption between model parameters and those with model parameters divided into multiple ordered groups are also derived. Several examples are presented to illustrate the alpha prior method. A simulation study based on a two-parameter regression model is performed to compare alpha priors with different values of α. A real example from an extracorporeal membrane oxygenation experiment demonstrates an application of the alpha prior.