For the problem of variable selection for the normal linear model, selection criteria such as , C p ,  and  have fixed dimensionality penalties. Such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical Bayes formulation. Based on this calibration, we propose empirical Bayes selection criteria that...

The Cp selection criterion is a popular method to choose the smoothing parameter in spline regression. Another widely used method is the generalized maximum likelihood (GML) derived from a normal-theory empirical Bayes framework. These two seemingly unrelated methods, have been shown in Efron (Ann. Statist. 29 (2001) 470) and Kou and Efron (J. Amer. Statist. Assoc. 97 (2002) 766) to be actually...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

In risk analysis based on Bayesian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfolio. When the prior knowledge is vague, the E-Bayesian and robust Bayesian analysis can be used to handle the uncertainty in specifying the prior distribution by considering a class of priors instead of a single prior. In th...

i n s u p p o r t i n g e n v i r o n m e n t a l s u s t a i n a b i l i t y, m a n a g i n g p r o d u c t r e t u r n s h a s b e c o m e a v e r y i m p o r t a n t a n d c h a l l e n g i n g i s s u e. r e s p o n d i n g t o t h i s t r e n d, r e s e a r c h e r s i n m a n y p a r t s o f t h e w o r l d h a v e c o n d u c t e d n u m e r o u s s t u d i e s i n r e v e r s e l o g i ...

When applying an unordered set of classification rules, the rules may assign more than one class to a particular example. Previous methods of resolving such conflicts between rules include using the most frequent class in the conflicting rules (as done in CN2) and using näıve Bayes to calculate the most probable class. An alternative way of solving this problem is presented in this paper: by ge...

Pourang Irani Visual Interfaces Laboratory University of New Brunswick Box 4400 Fredericton, NB Canada E3B 2A3 (506) 453-4566 [email protected] Colin Ware Data Visualization Research Lab Center for Coastal and Ocean Mapping University of New Hampshire Durham, NH 03824 (603) 862-1138 [email protected] Maureen Tingley Department of Mathematics University of New Brunswick Box 4400 Fredericto...