The Bayesian reliability estimation under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed to be fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of reliability by invoking the well-known theorem called ‘Resolution Iden...

Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive factorization theorem to situations with hidden variables. In the case when the underlying graph is a tree, we show that the vanishing ideal of the model is gen...

We used a computerized Bayesian algorithm to assist in the preoperative diagnosis of pulmonary lesions. One hundred consecutive patients who were undergoing exploratory thoracotomy for newly discovered pulmonary lesions were prospectively evaluated. The Bayesian model used a total of 44 preoperative clinical and roentgenographic factors to categorize the lesions as benign or malignant. The Baye...

A Bayesian network, or directed acyclic graphical model is a probabilistic graphical model that represents conditional dependencies and conditional independencies of a set of random variables. Each node is associated with a probability function that takes as input a particular set of values for the node’s parent variables and gives the probability of the variable represented by the node, condit...

K-means clustering algorithm is a method of cluster analysis which aims to partition n observations into clusters in which each observation belongs to the cluster with the nearest mean. It is one of the simplest unconfirmed learning algorithms that solve the well known clustering problem. It is similar to the hope maximization algorithm for mixtures of Gaussians in that they both attempt to fin...

Some recent papers were concerned with applicability of the Bayesian (statistical) approach to reconstruction of dynamic systems (DS) from experimental data. A significant merit of the approach is its universality. But, being correct in terms of meeting conditions of the underlying theorem, the Bayesian approach to reconstruction of DS is hard to realize in the most interesting case of noisy ch...

This paper proves that the revenue equivalence theorem ceases to hold for auctions without common knowledge about the agents' prior beliefs. That is, different auction forms yield different expected revenue. To prove this, an auction game is converted to a Bayesian decision problem with an infinite hierarchy of beliefs. A general solution for such Bayesian decision problems is proposed. The sol...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

We study nonparametric Bayesian models for reversible multidimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem the drift gradient vector field under approximation-theoretic conditions on induced prior invariant measure. The applied Gaussian priors and p-exponential priors, which are shown ...