Let X ∼ Np(θ, σIp) and W ∼ σχm, where both θ and σ are unknown, and X is independent of W . Optimal estimation of θ with unknown σ is a fundamental issue in applications but basic theoretical issues remain open. We consider estimation of θ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for θ are adm...

The mapping of geographical variation in disease occurrence plays an important role in assess ing environmental justice i e the equitable sharing of adverse e ects of pollution across socio demographic subpopulations Bayes and empirical Bayes methods can be used to obtain stable small area estimates while retaining geographic and demographic resolution In this study we fo cus on modeling spatia...

BACKGROUND While there is evidence that maternal exposure to benzene is associated with spina bifida in offspring, to our knowledge there have been no assessments to evaluate the role of multiple hazardous air pollutants (HAPs) simultaneously on the risk of this relatively common birth defect. In the current study, we evaluated the association between maternal exposure to HAPs identified by the...

The Tree Augmented Naı̈ve Bayes classifier is a type of probabilistic graphical model that can represent some feature dependencies. In this work, we propose a Hierarchical Redundancy Eliminated Tree Augmented Naı̈ve Bayes (HRE–TAN) algorithm, which considers removing the hierarchical redundancy during the classifier learning process, when coping with data containing hierarchically structured feat...

We consider the problems of hypothesis testing and model comparison under a flexible Bayesian linear regression model whose formulation is closely connected with the linear mixed effect model and the parametric models for Single Nucleotide Polymorphism (SNP) set analysis in genetic association studies. We derive a class of analytic approximate Bayes factors and illustrate their connections with...

Naive Bayes models have been very popular in several classification tasks. In this paper we study the application of these models to classification tasks where the data is sparse i.e., a large number of possible outcomes do not appear in the data. Traditionally point estimates of the model parameters and in particular, point estimates based on the Laplace’s rule have been popular for such spars...