The Bayesian interpretation of probability is one of two broad categories of interpretations. Bayesian inference updates knowledge about unknowns, parameters, with information from data. The LaplacesDemon package in R enables Bayesian inference, and this vignette provides an introduction to the topic. This article introduces Bayes’ theorem, model-based Bayesian inference, components of Bayesian...

Electric potential measurement technique (tomography) was introduced as a nondestructive method to evaluate concrete properties and durability. In this study, numerical meshless method was developed to solve a differential equation which simulates electric potential distribution for concrete with inclusion in two dimensions. Therefore, concrete samples with iron block inclusion in different loc...

Online social networks create significant challenges to computer scientists, physicists, and sociologists alike, for their massive size, fast evolution, and uncharted potential for social computing. One particular problem that has interested us is community identification. In this review, we focus on “community detection in social networks” through different approaches and techniques mainly Bay...

Belief consolidation schemes in AI can be viewed as three dimensional languages, consisting of a syntax (e.g. probabilities or certainty Factors), a calculus (e.g. Bayesian rules or CF combination rules), and a semantics (i.e. cognitive interpretations of competing formalisms). This paper studies the underlying rationality of those languages on the syntax and calculus grounds. In particular, th...

We prove general exponential moment inequalities for averages of [0,1]valued iid random variables and use them to tighten the PAC Bayesian Theorem. The logarithmic dependence on the sample count in the enumerator of the PAC Bayesian bound is halved.

This essay is meant for a reader who has attained a firm grasp of Bayes' Theorem. An introduction to Bayes' Theorem may be found in An Intuitive Explanation of Bayesian Reasoning (Yudkowsky 2003). You should easily recognize, and intuitively understand,

On the basis of examining the existing restricted Bayesian network classifiers, a new Bayes-theorem-based and more strictly restricted Bayesian-network-based classification model DLBAN is proposed, which can be viewed as a double-level Bayesian network augmented naive Bayes classification. The experimental results show that the DLBAN classifier is better than the TAN classifier in the most cases.

We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanation to the Bayesian Occam’s razor criteria, under the assumption that the data ...

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes’ theorem to complex problems. In the application of Bayesian networks, most of the work is related to probabilistic inferences. Any variable updating in any node of Bayesi...