This research proposal aims to develop novel statistical methodology for objective Bayesian model selection in generalized regression models. There is now a large literature on automatic and objective Bayesian model selection for the linear model, which unburden the statistician from eliciting manually the parameter priors for all models in the absence of substantive prior information (Berger and Pericchi, 2001). The g-prior, usually attributed to Zellner (1986) but already used by Copas (1983), is the standard choice for the regression coefficients. However, for generalized linear models and further extensions, there are computational and conceptual problems with the g-prior approach. Similarly, research on the appropriate prior distribution on the model space and the selection of the “best” model has been done mainly in the linear model, e. g. Scott and Berger (2006, 2010) and Barbieri and Berger (2004).
We will fill these gaps and will extend the scope of objective Bayesian model selection to generalized regression models.
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