The present article provides a very basic introduction to Bayes’ theorem and its potential implications for medical research. This introduction was written to be accessible to medical researchers without much mathematical background in general or without much background in Bayesian mathematics specifically. I prove Bayesian equations from very basic probability theorems and also show how these ...

The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should n...

Bayesian inference is an important technique throughout statistics. The essence of Beyesian inference is to derive the posterior belief updated from prior belief by the learned information, which is a set of differentially private answers under differential privacy. Although Bayesian inference can be used in a variety of applications, it becomes theoretically hard to solve when the number of di...

2013 marked the 250th anniversary of the presentation of Bayes’ theorem by the philosopher Richard Price. Thomas Bayes was a figure little known in his own time, but in the 20th century the theorem that bears his name became widely used in many fields of research. The Bayes theorem is the basis of the so-called Bayesian methods, an approach to statistical inference that allows studies to incorp...

We propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to perform the Bayesian computation. We find that the results obtained using this method are not only ...

A Bayesian model is nonparametric if its parameter space has infinite dimension; typical choices are spaces of discrete measures and Hilbert spaces. We consider the construction of nonparametric priors when the parameter takes values in a more general functional space. We (i) give a Prokhorov-type representation result for nonparametric Bayesian models; (ii) show how certain tractability proper...

Intrusion detection systems (IDSs) have become a critical part of security systems. The goal of an intrusion detection system is to identify intrusion effectively and accurately. However, the performance of misuse intrusion detection system (MIDS) or anomaly intrusion detection system (AIDS) is not satisfying. In this paper, we study the issue of building a compound intrusion detection model, w...

We obtain the strong law of large numbers, Glivenko-Cantelli theorem, central limit functional theorem for various Bayesian nonparametric priors which include stick-breaking process with general weights, two-parameter Poisson-Dirichlet process, normalized inverse Gaussian generalized gamma and Dirichlet process. For we introduce two conditions such that hold. Except in case since finite dimensi...

Belief updating schemes in artificial intelligence may be viewed as three dimensional languages, consisting of a syntax (e.g. probabilities or certainty factors), a calculus (e.g. Bayesian or CF combination rules), and a semantics (i.e. cognitive interpretations of competing formalisms). This paper studies the rational scope of those languages on the syntax and calculus grounds. In particular, ...

Challenging optimization problems, which elude acceptable solution via conventional calculus methods, arise commonly in different areas of industrial design and practice. Hard optimization problems are those who manifest the following behavior: a) high number of independent input variables; b) very complex or irregular multi-modal fitness; c) computational expensive fitness evaluation. This pap...