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A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.

Probabilistic packet dropping in dependence on the instantaneous buffer queue level at the pre-arrival epoch is one of Active Queue Management (AQM) mechanisms, used in IP routers for avoiding the risk of buffer overflow and for stabilizing the intensity of the input stream of packets. In the paper transient behavior of departure process h(t), counting packets which leave the service station before the fixed time t, is investigated in the GI/M/1/N queueing model with AQM-type probabilistic packet dropping. Using the approach based on the paradigm of embedded Markov chain and the total probability law, a system of Volterra integral equations for the distribution of h(t), conditioned by the number of packets present in the system initially, is obtained. The solution of the corresponding system written for 2-fold transforms of conditional distributions of h(t) is derived using the linear algebra approach. Illustrative numerical examples are attached as well.

In the analysis of seismic vulnerability curve based on double damage criterion, the randomness of structural parameter and randomness of seismic should be considered. Firstly, the distribution characteristics of structure capability and seismic demand are obtained based on IDA and PUSHOVER, secondly, the vulnerability of the bridge is gained based on ANN and MC and a vulnerability curve according to this bridge and seismic is drawn. Finally, the analysis for a continuous bridge is displayed as an example, and parametric analysis for the effect of β is done, which reflects the bridge vulnerability overall from the point of total probability, and in order to reduce the discreteness, large value of β are suggested.

We show that paradoxical consequences of violations of Bell’s inequality are induced by the use of an unsuitable probabilistic description for the EPR‐Bohm‐Bell experiment. The conventional description (due to Bell) is based on a combination of statistical data collected for different settings of polarization beam splitters (PBSs). In fact, such data consists of some conditional probabilities which only partially define a probability space. Ignoring this conditioning leads to apparent contradictions in the classical probabilistic model (due to Kolmogorov). We show how to make a completely consistent probabilistic model by taking into account the probabilities of selecting the settings of the PBSs. Our model matches both the experimental data and is consistent with classical probability theory.

The forward neutron production in the ep collisions at 300 GeV measured by the H1 and ZEUS Collaborations at DESY has been used to estimate the total probability for the proton fluctuation into nπ+ and pπ0. The probability found is on the order of the 30%. This number is compared with the numbers of obtained for the probability of quark fluctuation into π+ from several alternative DIS processes (Gottfried sum rule, polarized structure function) and the axial‐vector coupling constant, where the pion fluctuation is believed to play an important role.

General theoretical principles that enable the derivation of prior probabilities are of interest both in practical data analysis and, more broadly, in the foundations of probability theory. In this paper, it is shown that the general rule for the assignment of priors proposed by Jeffreys can be obtained from, and is logically equivalent to, an intuitively reasonable information‐theoretical invariance principle Some of the implications for the priors proposed by Hartigan, Jaynes, and Skilling, are also discussed.

This paper surveys some of the recent results that have been obtained in fuzzy quantum probability theory. In this theory fuzzy events are represented by quantum effects and fuzzy random variables are represented by quantum measurements. Probabilities, conditional probabilities and sequential products of effects are discussed. The relationship between the law of total probability and compatibility of measurements is treated. Results concerning independent effects are given. Finally, properties of the sequential product, almost sharp effects and nearly sharp effects are discussed.

Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some traditional results in statistical inference. However, as far as the authors know, there is no work on this subject, except [1]. The results of this paper can be extended to other branches of probability and statistics. In Section 2 total probability formula based on median is defined and its basic properties are proved. A few applications of this new tool are given in Section 3., Comment: Presented at the 23th Int. worskhop on Bayesian and Maximum Entropy methods (MaxEnt23), Aug. 3-7, 2003, Jackson Hole, USA

Correlation between neuron activity, a form of noise, is of vital importance for the nervous system to carry out computation. Here we present a concrete example to demonstrate the advantages of correlated neuronal computation. Suppose that a neuron receives two signals masked by random noise. After neuronal transformation, will the masked signals become more separable or more mixed? We prove that with positive correlations between input singles, the output becomes more separable. The critical value at which the total probability of misclassification is zero is analytically obtained and is independent of model parameters.

Probability is an aggregatible property of logical propositions; the theory of probability, including even its numerical representability, can be developed from the theory of aggregatibility. The new axiomatization given here improves the well-known axiomatizations of Cox and of Kolmogorov. It explains why probabilities can be represented quantitatively; it shows how nonquantitative systems of probability differ from the standard system, and what has to be given up when one attempts to generalize; it shows that the path from propositional logic to probability theory can be surprisingly direct.

The use of a radioisotope thermoelectric generator fueled with plutonium‐238 dioxide on the Space Shuttle‐launched Ulysses mission implies some level of risk due to potential accidents. This paper describes the method used to quantify risks in the Ulysses mission Final Safety Analysis Report prepared for the U.S. Department of Energy. The starting point for the analysis described herein is following input of source term probability distributions from the General Electric Company. A Monte Carlo technique is used to develop probability distributions of radiological consequences for a range of accident scenarios thoughout the mission. Factors affecting radiological consequences are identified, the probability distribution of the effect of each factor determined, and the functional relationship among all the factors established. The probability distributions of all the factor effects are then combined using a Monte Carlo technique. The results of the analysis are presented in terms of complementary cumulative distribution functions (CCDF) by mission sub‐phase, phase, and the overall mission. The CCDFs show the total probability that consequences (calculated health effects) would be equal to or greater than a given value.

A model of an associative neural network is developed in which the state of each node is described by a probability density. The realization of the network is based on the pairwise joint probabilities obtained from a training set of states. A positive definite ‘‘energy’’ functional of the probabilities may be constructed from Bayes’ rule of statistical inference. When the states of some of the nodes are fixed as constraints, the minimization of the energy yields a set of probability functions which is consistent with the original pairwise correlations.