Radio network modeling using criticality and conditional probability theory

1991 ◽  
Vol 31 (5) ◽  
pp. 1045
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Network Modeling ◽  
Radio Network

scholarly journals Disintegration and Bayesian inversion via string diagrams

2019 ◽  
Vol 29 (7) ◽  
pp. 938-971 ◽  
Author(s):  
Kenta Cho ◽  
Bart Jacobs
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Opposite Direction ◽  
Bayesian Inversion ◽  
Conditional Probabilities ◽  
Discrete Probability ◽  
Joint State

AbstractThe notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability – via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

scholarly journals An Application of Possibilistic Moments of Nonlinear Type of Fuzzy Numbers in Supply Chain Management

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Srimantoorao S. Appadoo ◽  
Yuvraj Gajpal ◽  
Amit Kumar
Keyword(s):  
Stochastic Process ◽  
Probability Theory ◽  
Supply Chain ◽  
Fuzzy Numbers ◽  
Network Modeling ◽  
Inventory Model ◽  
Supply Chain Network ◽  
International Level ◽  
Chain Management ◽  
Network Failure

The supply chain (SC) network is prone to disturbance due to various uncertainties associated with their subsystems. The COVID-19 outbreak has exposed the global vulnerability of the supply chain network. The current pandemic has severely affected almost every SC network because its members are situated at the international level. One of the reasons for SC network failure is the deterministic assumptions of different parameters. A realistic SC network model requires the use of the uncertain value of the parameters, which can be further captured by fuzzy numbers. This paper discusses the possibilistic moment of several nonlinear types of fuzzy numbers that are important for SC network modeling. We give closed-form possibilistic moments’ expression for various types of fuzzy numbers that are very similar to the moment’s properties in probability theory and stochastic process. We then illustrate the application of proposed fuzzy numbers by solving an inventory model. This paper also provides results related to the EPQ inventory model in a fuzzy possibilistic setup.

Some New Aspects of Slamming Probability Theory

1978 ◽  
Vol 22 (03) ◽  
pp. 186-192
Author(s):  
Harilaos N. Psaraftis
Keyword(s):  
Probability Theory ◽  
Poisson Process ◽  
Conditional Probability ◽  
Systematic Investigation ◽  
Unconditional Probability ◽  
Deck Wetness

A systematic investigation of some probabilistic aspects of slamming is presented. This investigation includes the assessment of the unconditional probability of slamming at a random instant of time; the estimation of the conditional probability of slamming at a given instant after a particular slam; and the consequent rejection of the hypothesis that slamming is a Poisson process. In addition, a procedure to approximate the distribution of slamming interarrival times2 is presented. Finally, new slamming statistics, obtainable from the theory of this work, are presented and compared with the existing slamming criteria. The theory of this paper can be readily applied to other seakeeping events such as deck wetness, keel emergence, and propeller racing.

Probability for Everyone—Even Philosophers

2017 ◽  
Author(s):  
Alan Hájek ◽  
Christopher Hitchcock
Keyword(s):  
Probability Theory ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Conditional Probability ◽  
Central Limit ◽  
Measure Theory ◽  
Bayes Theorem ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
Key Concepts

In this chapter the basics of probability theory are introduced, with particular attention to those topics that are most important for applications in philosophy. The formalism is described in two passes. The first presents finite probability, which suffices for most philosophical discussions of probability. The second presents measure theory, which is needed for applications involving infinities or limits. Key concepts such as conditional probability, probabilistic independence, random variables, and expectation are defined. In addition, several important theorems, including Bayes’ theorem, the weak and strong laws of large numbers, and the central limit theorem are defined. Along the way, several familiar puzzles or paradoxes involving probability are discussed.

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