In the rough set theory with every decision rule two conditional probabilities, called certainty and co erage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. It is shown that these two factors satisfy the Bayes’ theorem. The Bayes’ theorem in our case simply shows some relationship in the data...

The class-specific method (CSM) is an approach for constructing classifiers with class-dependent features that blends signal processing with classifcation theory. CSM is based on the mathematical identity called the probability density function (PDF) projection theorem that extends classical Bayesian theory. In contrast to conventional classifiers, feature extraction is an integral part of the ...

In this paper, we propose a computational data structure based on the binary join tree where the independence relations of the original directed evidential networks (DEVN) are maintained. The proposed solution uses disjunctive rule of combination (DRC) and generalized Bayesian theorem (GBT), which make possible the use of the conditional belief functions directly for reasoning in the DEVN.

OBJECTIVES The observed posterior probability distributions regarding the benefits of surgery for otitis media with effusion (OME) with expected probability distributions, using Bayes' theorem are compared. METHODS Postal questionnaires were used to assess prior and posterior probability distributions among ear-nose-throat (ENT) surgeons in the Netherlands. RESULTS In their prior probabilit...

With the continued growth and proliferation of Web services and Web based information systems, the volumes of user data have reached astronomical proportions. Analyzing such data using Web Usage Mining can help to determine the visiting interests or needs of the web user. As web log is incremental in nature, it becomes a crucial issue to predict exactly the ways how users browse websites. It is...

this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.

Many problems of statistics are naturally formulated in terms of the predictive distribution of an as yet unobserved random variable, rather than the more traditional questions of parameter estimation and hypothesis testing. Both frequentist and Bayesian approaches to predictive inference may be considered, but it is argued that the Bayesian approach is more general and exible. This leads us to...

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes’ theorem, imposing posterior regularization is arguably more direct and in some cases can be more natural and easier. In this paper, we present regula...

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the ...

Mathematical statistics uses two major paradigms, conventional (or frequentist), and Bayesian. Bayesian methods provide a complete paradigm for both statistical inference and decision making under uncertainty. Bayesian methods may be derived from an axiomatic system, and hence provide a general, coherent methodology. Bayesian methods contain as particular cases many of the more often used frequ...