Data are frequently not precise numbers but more or less non-precise, also called fuzzy. Moreover a-priori information in Bayesian inference is usually not available as a precise probability distribution. In case of fuzzy data and fuzzy a-priori information Bayes' theorem has to be generalized. There are different approaches for a generalization of Bayes' theorem but most of them don't keep the...

In a probability-based reasoning system, Bayes’ theorem and its variations are often used to revise the system’s beliefs. However, if the explicit conditions and the implicit conditions of probability assignments are properly distinguished, it follows that Bayes’ theorem is not a generally applicable revision rule. Upon properly distinguishing belief revision from belief updating, we see that J...

A generalized envelope theorem is established for a Bayesian dynamic program problem. An application of the theorem is given in a Bayesian inventory management problem with unobserved lost sales. Specifically, we show that the optimal inventory level with unobserved lost sales is greater than the optimal inventory level with observed lost sales. We prove this result under the continuous demand ...

453 AbstractA Bayesian classifier is one of the most widely used classifiers which possess several properties that make it surprisingly useful and accurate. It is illustrated that performance of Bayesian learning in some cases is comparable with neural networks and decision trees. Bayesian theorem suggests a straight forward process which is not based on search methods. This is the major point ...

Bayesian networks are a popular class of graphical probabilistic models for researches and applications in the field of Artificial Intelligence. Bayesian network are built on Bayes’ theorem (16) and allow to represent a joint probability distribution over a set of variables in the network. In Bayesian probabilistic inference, the joint distribution over the set of variables in a Bayesian networ...

A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (vb) methods have emerged as a popular alternative to the classical Markov chain Monte Carlo (mcmc) methods. vb methods tend to be faster while achieving comparable predictive performance. However, there are few theoretical results around v...

Bayesian statistics, a currently controversial viewpoint concerning statistical inference, is based on a definition of probability as a particular measure of the opinions of ideally consistent people. Statistical inference is modification of these opinions in the light of evidence, and Bayes' theorem specifies how such modifications should be made. The tools of Bayesian statistics include the t...

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum likelihood estimates from corrupted or incomplete data. The convergence speed-up is an example of a noise benefit or"stochastic resonance"in statistical signal proce...

1 The Bayesian view of the Jury Theorem 1.1 Criticism on the Bayesian view Recall the model setup: let s ∈ {±1} be the true state of the world. We shall assume a uniform prior on s, that is, P (s = +) = P (s = −) =