Mathematical Models for the Diagnosis of Liver DiseasePROBLEMS ARISING IN THE USE OF CONDITIONAL PROBABILITY THEORY

QJM ◽  
1974 ◽  
Keyword(s):  
Probability Theory ◽  
Liver Disease ◽  
Mathematical Models ◽  
Conditional Probability

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 Safety of transport processes of the trucks determined by reliability.

2015 ◽  
Vol 2015 (2) ◽  
pp. 88-92
Author(s):  
Владимир Самусенко ◽  
Vladimir Samusenko ◽  
Наталия Сакович ◽  
Nataliya Sakovich ◽  
Евгений Христофоров ◽  
...  
Keyword(s):  
Probability Theory ◽  
Mathematical Models ◽  
Russian Federation ◽  
Transport Processes ◽  
The Russian Federation

In article questions of safety of transport processes on roads of the Russian Federation of the vehicles caused by reliability are considered. Authors considered activities on safety of the movement at design stages of the created car. For a solution authors used mathematical models on the basis of probability theory.

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.

scholarly journals A method of value measurement based on probability theory in economics

2021 ◽  
Author(s):  
Gang Xi ◽  
Xiaoyi Yang ◽  
Ming Xi
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Weighted Average ◽  
Random Variable ◽  
Conditional Probability Distribution ◽  
Mean And Variance ◽  
The Mean ◽  
New Perspective ◽  
Value Measurement ◽  
Quantitative Statistics

Abstract Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable, a price is the value of the good in terms of money, according to the price’s historical records, quantitative statistics and human experiences, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

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