ABSTRACT We develop a Bayesian procedure for the homogeneity testing problem of r populations using r× s contingency tables. The posterior probability of the homogeneity null hypothesis is calculated using a mixed prior distribution. The methodology consist of choosing an appropriate value of π0 for the mass assigned to the null and spreading the remainder, 1 − π0, over the alternative accordin...

This paper presents a general, fully Bayesian framework for sparse supervised-learning problems based on the horseshoe prior. The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used approaches for sparse Bayesian learning, including, among others, Laplacian priors (e.g. the LASSO) and Student-t priors (e.g. the rel...

Based on Bayesian network theorem, the paper proposed the novel trust model of P2P network named Trust-BT. The novel new Trust-BT model is based on the P2P network nodes’ history of all types of transactions, prior experience, the use of Bayesian statistical analysis methods calculate the global trust value of every network node, select the node with high trust value node transactions. The math...

Risk assessment is an essential component of genetic counseling and testing, and Bayesian analysis plays a central role in genetic risk assessment. Bayesian analysis allows calculation of the probability of a particular hypothesis, either disease or carrier status, based on family information and/or genetic test results. Genetic risk should be assessed as accurately as possible for family decis...

This paper provides an elementary tutorial overview of Bayesian inference and its potential for application in aerospace experimentation in general and wind tunnel testing in particular. Bayes’ Theorem is reviewed and examples are provided to illustrate how it can be applied to objectively revise prior knowledge by incorporating insights subsequently obtained from additional observations, resul...

Pawlak recently introduced rough set flow graphs (RSFGs) as a graphical framework for reasoning from data. Each rule is associated with three coefficients, which have been shown to satisfy Bayes’ theorem. Thereby, RSFGs provide a new perspective on Bayesian inference methodology. In this paper, we show that inference in RSFGs takes polynomial time with respect to the largest domain of the varia...

This paper represents a new context-aware learning system to provide services in ubiquitous computing environment. The aim is to precisely decide which services each user provides. To achieve this goal, we design a preprocessing method (i.e., context modeling) to obtain good information which represents user’s characteristics from context-aware information (i.e., user profiles) which consists o...

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held inte...

We present distribution-free generalization error bounds which apply to a wide class of approximate Bayesian Gaussian process classification (GPC) techniques, powerful nonparametric learning methods similar to Support Vector machines. The bounds use the PACBayesian theorem [8] for which we provide a simplified proof, leading to new insights into its relation to traditional VC type union bound t...

Readers of The American Statistician may recognize in my title a salute to David Moore’s (1997) “Bayes for Beginners? Some Reasons to Hesitate.” In his paper Moore detailed four main reasons why he judged it at best premature to teach Bayesian methods in a first statistics course. Since the publication of Moore’s paper, more than ten years have passed, during which time our profession has been ...