A Mean Probability Event for a Set of Events (original) (raw)
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Eventology of multivariate statistics Eventology and mathematical eventology Philosophical eventology and philosophy of probability Practical eventology Eventology of safety Eventological economics and psychology Mathematics in the humanities, socio-economic and natural sciences Financial and actuarial mathematics Multivariate statistical analysis Multivariate complex analysis Decision-making under risk and uncertainty Risk measurement and risk models Theory of fuzzy events and generalized theory of uncertainty System analysis and events management EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem With topics from quantum physics, probability and believability to economics, sociology, and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts, and ideas on the axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem. Eventology of experience and chance Believability theory and statistics of experience Probability theory and statistics of chance Axiomatizing experience and chance
Eventology of Random-Fuzzy Events
2005
A brief introduction to the eventology, which has originated recently as a new line of probability theory. This line studies eventological motion of random-fuzzy events (evento-logical motion of events motion of matter or motion of mind changing the evento-logical distributions), ...
Proceedings of the XII FAMES 2013 Conference on Financial and Actuarial Maths and Eventology of Safety, 2013
Financial and actuarial mathematics Eventology of multivariate ststistics Eventology of safety Eventology and mathematical eventology Philosophical eventology and philosophy of probability Eventology and the new humanity Practical eventology Eventological economics and psychology Eventological problems of artificial intelligence Converging sciences and technologies Mathematics in the humanities, socio-economic and natural sciences Probability theory and statistics Multivariate statistical analysis Decision-making under risk and uncertainty Risk measurement and risk models Theory of fuzzy events and generalized theory of uncertainty Mathematical onset to chaos in economy System analysis and events management
Eventologically multivariate extensions of probability theory’s limit theorems
Eventologically multivariate extensions of probability theory’s limit theorems are proposed. Eventologically multivariate version of limit theorems extends its classical probabilistic interpretation and involves into its structure of dependencies of arbitrary set of events which appears in sequence of independent tests.
Eventology versus contemporary theories of uncertainty
The XII International EM'2009 Conference, Program and Abstracts, Krasnoyarsk, Sib. Fed. Univ., 13-27, 2009
The development of probability theory together with the Bayesian approach in the three last centuries is caused by two factors: the variability of the physical phenomena and partial ignorance about them. As now it is standard to believe [Dubois, 2007], the nature of these key factors is so various, that their descriptions are required special uncertainty theories, which differ from the probability theory and the Bayesian credo, and provide a better account of the various facets of uncertainty by putting together probabilistic and set-valued representations of information to catch a distinction between variability and ignorance. Eventology [Vorobyev, 2007], a new direction of probability theory and philosophy, offers the original event approach to the description of variability and ignorance, entering an agent, together with his/her beliefs, directly in the frameworks of scientific research in the form of eventological distribution of his/her own events. This allows eventology, by putting together probabilistic and set-event representation of information and philosophical concept of event as co-being [Bakhtin, 1920], to provide a unified strong account of various aspects of uncertainty catching distinction between variability and ignorance and opening an opportunity to define imprecise probability as a probability of imprecise event in the mathematical frameworks of Kolmogorov's probability theory [Kolmogorov, 1933]. For further development of this topic, see my later works: https://www.academia.edu/34390291/, https://www.academia.edu/34373279/, https://www.academia.edu/34357251/
The logic of uncertainty as a logic of experience and chance and the co∼event-based Bayes' theorem
The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters. Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.
Discrete multivariate distributions
2008
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson distributions. Accordingly to eventology new laws take into account full distribution of events. Also, in article its characteristics and properties are described
An urban passenger transportation problem is researched. Municipal authorities and passengers are regarded as participants in the transportation system. The municipal authorities have to optimize road capacity and public transport frequency. Passengers travel mode choice is based on logit model. Traffic congestion is described by Greenshields equation. The existence of Nash equilibrium between municipal authorities and passengers is proved. The numerical example characterizing the influence of the parameters on the problem solution is given.