Oleg Yu Vorobyev | Siberian Federal University (original) (raw)
Books by Oleg Yu Vorobyev
266 pages from Eventology, 2007
Chapter 14 EVENTOLOGICAL MODELS IN PSYCHOLOGY, Chapter 7 FRECHET's SAIL and WIND, Chapter 4 A SET... more Chapter 14 EVENTOLOGICAL MODELS IN PSYCHOLOGY,
Chapter 7 FRECHET's SAIL and WIND,
Chapter 4 A SET OF EVENTS,
Chapter 10 THEORY OF FUZZY EVENTS,
Chapter 16 EVENTOLOGICAL THEORY OF DECISION MAKING,
Chapter 11 EVENTOLOGICAL PORTFOLIO ANALYSIS,
contents, prologue, epilogue, and chapters 1, 2, and 3 from the book about the eventology ~ a science about events and its applications to problems of management of sets of events ~ a new direction in philosophy, mathematics and event management.
This book outlines ideas that inspired me while I was trying to build a new event science, eventology. Not each of these ideas was developed, but all of them inspired me in the construction of eventology, and then in the discovery of a revolutionary theory of experience and chance, co~eventum mechanics. (see, for example, https://www.academia.edu/34357251,
https://www.academia.edu/34373279,
https://www.academia.edu/34390291,
https://www.academia.edu/38368776,
https://www.academia.edu/38154263 and so on).
The book about the eventology ~ a science about events and its applications to problems of manage... more The book about the eventology ~ a science about events and its applications to problems of management of sets of events ~ a new direction in philosophy, mathematics and event management (see English version of the book: https://www.academia.edu/38605343/).
This book outlines ideas that inspired me while I was trying to build a new event science, eventology. Not each of these ideas was developed, but all of them inspired me in the construction of eventology, and then in the discovery of a revolutionary theory of experience and chance, co~eventum mechanics. (see, for example, https://www.academia.edu/34357251,
https://www.academia.edu/34373279,
https://www.academia.edu/34390291,
https://www.academia.edu/38368776,
https://www.academia.edu/38154263 and so on).
Conferences by Oleg Yu Vorobyev
Most likely, most of the results of this article were pondered, realized and proven by many. Howe... more Most likely, most of the results of this article were pondered, realized and proven by many. However, I present them in a new way for many, so that the connection between multivariate cumulative distribution functions (cdfs) of random variables and event-probability distributions (epds) of a set of events becomes quite obvious. To do this, I use a couple of new tricks. One of these is called the p-indicator of an event, which differs significantly from the classical indicator of an event, it makes sense only for half-rare events (another trick), which, however, does not detract from the generality of its application (it follows from the properties of half-rare events).
A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events,... more A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events, which leads to a new event-probability distribution of the new set of events that generates the same partition of the space of elementary outcomes but with a new distribution of the probability measure on it. When we talk here about events or a set of events, we do not mean any other meaning (philosophical, linguistical, etc., see for example: [2-8]) than a mathematical one, which these concepts have in the theory of probability and in the eventology [1]. In these theories, a set of events is given if its event-probability distribution is given. But in order to mathematically correctly define the probability distribution of a set of events, one must first define the probability space, i.e. the triple: the space of elementary outcomes, the algebra of events and the probability measure defined on the algebra of events. Everything that has been said applies to the concept of names of events, which is also understood here exclusively in the mathematical, more precisely, in the eventological [1] sense. At the same time, the eventological model of the event name proposed here is simple and can be widely used in practice to solve real-life problems.
Proceedings of the XIX Conference on FAMEMS and the V Workshop on Hilbert’s Sixth Problem, Krasnoyarsk, Siberia, 2021
A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events,... more A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events, which leads to a new event-probability distribution of the new set of events that generates the same partition of the space of elementary outcomes but with a new distribution of the probability measure on it. When we talk here about events or a set of events, we do not mean any other meaning (philosophical, linguistical, etc., see for example: [2-8]) than a mathematical one, which these concepts have in the theory of probability and in the eventology [1]. In these theories, a set of events is given if its event-probability distribution is given. But in order to mathematically correctly define the probability distribution of a set of events, one must first define the probability space, i.e. the triple: the space of elementary outcomes, the algebra of events and the probability measure defined on the algebra of events. Everything that has been said applies to the concept of names of events, which is also understood here exclusively in the mathematical, more precisely, in the eventological [1] sense. At the same time, the eventological model of the event name proposed here is simple and can be widely used in practice to solve real-life problems.
Most likely, most of the results of this article were pondered, realized and proven by many. Howe... more Most likely, most of the results of this article were pondered, realized and proven by many. However, I present them in a new way for many, so that the connection between multivariate cumulative distribution functions (cdfs) of random variables and event-probability distributions (epds) of a set of events becomes quite obvious. To do this, I use a couple of new tricks. One of these is called the p-indicator of an event, which differs significantly from the classical indicator of an event, it makes sense only for half-rare events (another trick), which, however, does not detract from the generality of its application (it follows from the properties of half-rare events).
XX FAMEMS'2021 Conference and the VI Workshop on Hilbert's Sixth Problem, Krasnoyarsk: SFU, 2021
Invitation Ministry of Education and Science of RF Institute of Mathematics and Computer Science... more Invitation
Ministry of Education and Science of RF
Institute of Mathematics and Computer Science
Siberian Federal University
XX
Conference
FINANCIAL and ACTUARIAL MATHEMTAICS
EVENTOLOGY of MULTIVARIATE STATISTICS
VI
Workshop
EVENTOLOGY of EXPERIENCE and CHANCE
HILBERT’s SIXTH PROBLEM
FAMEMS∼EEC∼H’s6P’2021
17 December 2021, Krasnoyarsk
FAMEMS’2021 ∼ Conference:
Themes of the FAMEMS include following directions, but are not limited by them exclusively. Any works with original
ideas are welcomed which induce application of mathematical and eventological methods in the most various areas.
Financial and actuarial mathematics
Mathematics in the humanities, socio-economic and natural sciences
Probability theory and statistics
Multivariate statistical analysis
Eventology of multivariate statistics
Co∼eventum mechanics
Theory of experience and chance
Eventology of safety
Eventology of risk and decision-making under risk and uncertainty
Philosophy of probability and event
Eventological economics and psychology
Eventological problems of artificial intelligence
Eventological aspects of quantum mechanics information theory
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∼H’s6P’2021 ∼ 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 co∼eventum mechanics and mathematical theories of experience and chance.
Topics of discussion include the results, thoughts and ideas on 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
Important dates:
November∼December 2021 — deadline for papers, and sessions
Instructions:
http://fam.conf.sfu-kras.ru/submission-e.php
Proceedings of the XVIII FAMEMS’2019 Conference, Part 1:
https://www.academia.edu/62707163/
Proceedings of the XVIII FAMEMS’2019 Conference, Part 2:
https://www.academia.edu/43861381/
Proceedings of the XIX FAMEMS’2020 Conference:
https://www.academia.edu/62731634/
Set functions and their summation are briefly considered in one important special case when the s... more Set functions and their summation are briefly considered in one important special case when the sets are the sets of Kolmogorov events [1-4].
Proceedings of the FAMEMs-2020 Conference, Krasnoyarsk, SFU Press, 2020
Set functions and their summation are briefly considered in one important special case when the s... more Set functions and their summation are briefly considered in one important special case when the sets are the sets of Kolmogorov events [1].
Möbius inversion formulas for the event-probability distributions of a set of events [1] are cons... more Möbius inversion formulas for the event-probability distributions of a set of events [1] are considered.
Proceedings of the XIII FAMEMS-2014 Conference, Krasnoyarsk, Siberian Federal University Press., 2014
We consider the notion of set-distance of NNN-set of events, characterizing an inconsistency of i... more We consider the notion of set-distance of NNN-set of events, characterizing an inconsistency of its events, and its extension up to an (N+1)(N+1)(N+1)-family of set-distances of different orders which are called set-distograms, characterizes the distribution of inconsistency of events relative to the power of subsets of the given set of events and serves as a convenient tool for detailed measurement of the inconsistency of a set of events.
Examples of set-distograms for several types of event-probability distributions of sets of events with different structures of consistency and inconsistency are given.
Attention is drawn to the fact that all three characteristics of an event: entropy, information, ... more Attention is drawn to the fact that all three characteristics of an event: entropy, information, and probability, depend on the observer of this event in the phenomenological sense, and not only because of the statistical errors of observation.
Keywords: Probability, entropy, information, observer, observation, Bertrand’s paradox, quantum contextuality.
Here an improved generalization of Feynman's paradox of negative probabilities [1, 2] for observi... more Here an improved generalization of Feynman's paradox of negative probabilities [1, 2] for observing three events is considered. This version of the paradox is directly related to the theory of quantum computing. Imagine a triangular room with three windows (see Fig. 1), where there are three chairs, on each of which a person can seat [3]. In any of the windows, an observer can see only the corresponding pair of chairs. It is known that if the observer looks at a window (to make a pair observation), the picture will be in the probabilistic sense the same for all windows: only one chair from the observed pair is occupied with a probability of 1/2, and there are never busy or free both chairs at once. Paradoxically, existing theories based on Kolmogorov's probability theory do not answer the question that naturally arises after such pairs of observations of three events: "What is really happening in a triangular room, how many people are there and with what is the probability distribution they are sitting on three chairs?". See also a random variable approach in [4, N.N.Vorob'ev, 1962].
The Rashomon effect occurs when an event is given contradictory interpretations by the individual... more The Rashomon effect occurs when an event is given contradictory interpretations by the individuals involved. The effect is named after Akira Kurosawa's 1950 film Rashomon, in which a murder is described in four contradictory ways by four witnesses [1]. The term addresses the motives, mechanism and occurrences of the reporting on the circumstance and addresses contested interpretations of events, the existence of disagreements regarding the evidence of events and subjectivity versus objectivity in human perception, memory and reporting. Lurking behind the theory of experience and chance, co∼eventum mechanics [2, 3, 4], and our modern understanding of mind and matter is the simple idea of co∼event. And among scientists, there is growing confidence that focusing on a co∼event is becoming more and more productive than it once was. Here we consider the co∼eventum mechanistic approach with the co∼eventum mechanistic Bayesian theorems [5] to analyze the Rashomon case in forensics.
For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it... more For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼ventum mechanics in the most approachable way. The main objective of co∼eventum mechanics and eventology [1] is the penetration of a new event-based language into all scientific and technological spheres and the development of the ability of the eventological potential of science and technology to transform the objects of study by event-based way, the formation of an interdisciplinary eventological paradigm that unifies, in the first place, socio-humanitarian, ecological, psycho-economic and other spheres, where scientific and technological research is difficult to imagine without including the observer in the subject of research, as well as the natural sciences in which the understanding of the impossibility of completely separating the subject of research from the observer has long been maturing. This is what I'm trying to do in this work. You yourself, or what is the same, your experience is such "coin" that, while you aren't questioned, it rotates all the time in "free light". And only when you answer the question the "coin" falls on one of the sides: "Yes" or "No" with the believability that your experience tells you.
Proceedings of the XIX FAMEMS'2020 Conference and the V Workshop on Hilbert's Sixth Problem, Krasnoyarsk: SFU, 2020
The theory of symmetric events, which was first published in [1] and which turned out to be usefu... more The theory of symmetric events, which was first published in [1] and which turned out to be useful in studying the relationship between eventological theory [2] and probability theory, is presented from the modern eventological point of view.
The dependence in modern directions of the theory of probability is the dependence, first of all, between random variables, i.e. between one-variate distribution functions.
It is quite clear that this dependence is generated by the dependence between the events on which the random variables are determined. The theory of symmetric events allows us to study in detail at the event level not only this dependence, which is traditionally studied in probability theory but also opens up a new opportunity to study how the form of each one-variate distribution function is determined by the structure of the dependencies of the set of symmetric events that determines this one-variate distribution function.
The fact is that in the theory of symmetric events each set of symmetric events has its own upper indicator, which is a pseudo-inverse function of the one-variate distribution function of this indicator.
Thus, the upper indicator of each set of symmetric events defines some one-variate distribution function.
This theory also shows that the range of different structures of dependencies of symmetric events is so wide that it covers the entire range of different types of one-variate distribution functions, which is determined by five reference distribution functions: from a degenerate distribution through binomial, equiprobable, and anti-binomial (this is a completely new distribution function that has yet to be studied in detail). to the distribution of a Boolean random variable. In this case, the degenerate distribution is determined by the set of least intersecting symmetric events, the binomial distribution is determined by the set of independent events, the equiprobable distribution is determined by the set of symmetric events with a pseudo-equiprobable distribution, the anti-binomial distribution is determined by the set of anti-independent symmetric events, and the Boolean distribution - by a set of nested coincident symmetric events.
So, the set of symmetric events is a convenient and widely applicable model for studying the types of one-variate distribution functions and how these types are determined by the structure of dependencies of a given set of symmetric events. Moreover, to study the types of two-variate and multivariate distribution functions, generalized event models from two or more sets of symmetric events are suitable under the assumption that their union is also a set of symmetric events.
Thus, as it turned out if one set of symmetric events determines the form of a one-variate distribution function, then two or more sets of symmetric events determine two-variate and multivariate distribution functions. In other words, the dependencies between one-variate distribution functions are determined, i.e. determine what is determined by the copula in modern probability theory.
Consequently, the sets of symmetric events and their structure of dependencies are suitable both for modeling copula (a well-studied direction in modern probability theory), which determine multivariate distribution functions for given one-variate and for modeling types of one-variate distribution functions, which is a completely new direction that is missing in modern probability theory.
Proceedings of the XI International FAMES'2012 Conference. Oleg Vorobyev, ed. - Krasnoyarsk: SFU. - 423 p., 2012
An eventological model of a mean-probable event for a set of events is proposed, which has analog... more An eventological model of a mean-probable event for a set of events is proposed, which has analogies with the concept of a mean-measure set that we introduced earlier.
(see also in English https://www.academia.edu/2328936/)
Proc. of the XV Intern. FAMEMS-2016 Conf. on Financial and Actuarial Math and Eventology of Multivariate Statistics, Krasnoyarsk, SFU (Oleg Vorobyev ed.), 44-93, 2016
This work is the third, but not the last, in the cycle begun by the works \cite{Vorobyev2016famem... more This work is the third, but not the last, in the cycle begun by the works \cite{Vorobyev2016famems1, Vorobyev2016famems2} about the new
theory of experience and chance as the theory of co~events. Here I introduce the concepts of two co~event means, which serve as dual co~event characteristics of some co~event. The very idea of dual co~event means has become the development of two concepts: mean-measure set \cite{Vorobyev1984} and mean-probable event \cite{Vorobyev2012fames4, Vorobyev2013sfu}, which were first introduced as two independent characteristics of the set of events, so that then, within the framework of the theory of experience and chance, the idea can finally get the opportunity to appear as two dual faces of the same co~event. I must admit that, precisely, this idea, hopelessly long and lonely stood at the sources of an indecently long string of guesses and insights, did not tire of looming, beckoning to the new co~event description of the dual nature of uncertainty, which I called the theory of experience and chance or the certainty theory. The constructive final push to the idea of dual co~event means has become two surprisingly suitable examples, with which I was fortunate to get acquainted in 2015, each of which is based on the statistics of the experienced-random experiment in the form of a co~event.
Eventology, theory of experience and chance, event, co~event, experience, chance, to happen, to experience, to occur, probability, believability, mean-believable (mean-experienced) terraced bra-event, mean-probable (mean-possible) ket-event, mean-believable-probability (mean-experienced-possible) co~event, experienced-random experiment, dual event means, dual co~event means, bra-means, ket-means, Bayesian analysis, approval voting, forest approval voting.
Proceedings of the XVII Conference on FAMEMS and the III Workshop on Hilbert's sixth problem. Krasnoyarsk, SFU, 44-53, 2018
We live in the real world, at such a time and in such circumstances, when not only principles bu... more We live in the real world, at such a time and in such circumstances, when not only principles but also facts blur, become overgrown with lies and pretense. The endless cycle of our indefinite co∼being forces observers to look for tools capable of coping with the challenges of uncertainty world, which would make it possible to comprehend, express and measure vague principles, facts, lies, and pretense. However, note that we have always lived, we live and we will live in the world of co∼events which is mathematically controlled by the theory of experience and chance and the co∼eventum mechanics. The main tools of these new theories are two measures: probabilistic and believabilistic, which are intended to comprehend, express and measure our co∼eventum world. The probability measures the future chance of observation, the believability measures the past experience of an observer. This paper shows that these two measures are naturally related to each other in the co∼eventum mechanistic H-theorem, and this connection between the past uncertainty of experience and the future uncertainty of chance is expressed using the Gibbs distribution, which is based on the extreme entropy conditions.
A co∼eventum mechanistic generalization of the eventological H-theorem is proposed, which determines the extreme-entropy properties of Gibbs distributions in the co∼eventum mechanics where Gibbs distributions relate the past experience of observers with the future chance of observations. The co∼eventum mechanistic H-theorem, a co∼eventum generalization of the Boltzmann H-theorem from statistical mechanics, justifies the application of Gibbs distributions of co∼events minimizing relative entropy, as statistical models of the behavior of a rational subject, striving for an equilibrium co∼eventum choice between the past experience and the future chance in various spheres of her/his co∼being.
Fréchet bounds of the 1st kind for sets of events and their main properties are considered in mor... more Fréchet bounds of the 1st kind for sets of events and their main properties are considered in more detail than in [1]. The theorem on not more than two nonzero values of lower Fréchet-bounds of the 1st kind for a set of half-rare events is proved with the corollary on the analogous assertion for sets of events with arbitrary event-probability distributions.
Keywords: probability, event, set of events, event-probability distribution, set of half-rare events, Fréchet bounds of the 1st kind.
266 pages from Eventology, 2007
Chapter 14 EVENTOLOGICAL MODELS IN PSYCHOLOGY, Chapter 7 FRECHET's SAIL and WIND, Chapter 4 A SET... more Chapter 14 EVENTOLOGICAL MODELS IN PSYCHOLOGY,
Chapter 7 FRECHET's SAIL and WIND,
Chapter 4 A SET OF EVENTS,
Chapter 10 THEORY OF FUZZY EVENTS,
Chapter 16 EVENTOLOGICAL THEORY OF DECISION MAKING,
Chapter 11 EVENTOLOGICAL PORTFOLIO ANALYSIS,
contents, prologue, epilogue, and chapters 1, 2, and 3 from the book about the eventology ~ a science about events and its applications to problems of management of sets of events ~ a new direction in philosophy, mathematics and event management.
This book outlines ideas that inspired me while I was trying to build a new event science, eventology. Not each of these ideas was developed, but all of them inspired me in the construction of eventology, and then in the discovery of a revolutionary theory of experience and chance, co~eventum mechanics. (see, for example, https://www.academia.edu/34357251,
https://www.academia.edu/34373279,
https://www.academia.edu/34390291,
https://www.academia.edu/38368776,
https://www.academia.edu/38154263 and so on).
The book about the eventology ~ a science about events and its applications to problems of manage... more The book about the eventology ~ a science about events and its applications to problems of management of sets of events ~ a new direction in philosophy, mathematics and event management (see English version of the book: https://www.academia.edu/38605343/).
This book outlines ideas that inspired me while I was trying to build a new event science, eventology. Not each of these ideas was developed, but all of them inspired me in the construction of eventology, and then in the discovery of a revolutionary theory of experience and chance, co~eventum mechanics. (see, for example, https://www.academia.edu/34357251,
https://www.academia.edu/34373279,
https://www.academia.edu/34390291,
https://www.academia.edu/38368776,
https://www.academia.edu/38154263 and so on).
Most likely, most of the results of this article were pondered, realized and proven by many. Howe... more Most likely, most of the results of this article were pondered, realized and proven by many. However, I present them in a new way for many, so that the connection between multivariate cumulative distribution functions (cdfs) of random variables and event-probability distributions (epds) of a set of events becomes quite obvious. To do this, I use a couple of new tricks. One of these is called the p-indicator of an event, which differs significantly from the classical indicator of an event, it makes sense only for half-rare events (another trick), which, however, does not detract from the generality of its application (it follows from the properties of half-rare events).
A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events,... more A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events, which leads to a new event-probability distribution of the new set of events that generates the same partition of the space of elementary outcomes but with a new distribution of the probability measure on it. When we talk here about events or a set of events, we do not mean any other meaning (philosophical, linguistical, etc., see for example: [2-8]) than a mathematical one, which these concepts have in the theory of probability and in the eventology [1]. In these theories, a set of events is given if its event-probability distribution is given. But in order to mathematically correctly define the probability distribution of a set of events, one must first define the probability space, i.e. the triple: the space of elementary outcomes, the algebra of events and the probability measure defined on the algebra of events. Everything that has been said applies to the concept of names of events, which is also understood here exclusively in the mathematical, more precisely, in the eventological [1] sense. At the same time, the eventological model of the event name proposed here is simple and can be widely used in practice to solve real-life problems.
Proceedings of the XIX Conference on FAMEMS and the V Workshop on Hilbert’s Sixth Problem, Krasnoyarsk, Siberia, 2021
A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events,... more A new tool for eventology [1] is considered-the permutation of the names (set-numbers) of events, which leads to a new event-probability distribution of the new set of events that generates the same partition of the space of elementary outcomes but with a new distribution of the probability measure on it. When we talk here about events or a set of events, we do not mean any other meaning (philosophical, linguistical, etc., see for example: [2-8]) than a mathematical one, which these concepts have in the theory of probability and in the eventology [1]. In these theories, a set of events is given if its event-probability distribution is given. But in order to mathematically correctly define the probability distribution of a set of events, one must first define the probability space, i.e. the triple: the space of elementary outcomes, the algebra of events and the probability measure defined on the algebra of events. Everything that has been said applies to the concept of names of events, which is also understood here exclusively in the mathematical, more precisely, in the eventological [1] sense. At the same time, the eventological model of the event name proposed here is simple and can be widely used in practice to solve real-life problems.
Most likely, most of the results of this article were pondered, realized and proven by many. Howe... more Most likely, most of the results of this article were pondered, realized and proven by many. However, I present them in a new way for many, so that the connection between multivariate cumulative distribution functions (cdfs) of random variables and event-probability distributions (epds) of a set of events becomes quite obvious. To do this, I use a couple of new tricks. One of these is called the p-indicator of an event, which differs significantly from the classical indicator of an event, it makes sense only for half-rare events (another trick), which, however, does not detract from the generality of its application (it follows from the properties of half-rare events).
XX FAMEMS'2021 Conference and the VI Workshop on Hilbert's Sixth Problem, Krasnoyarsk: SFU, 2021
Invitation Ministry of Education and Science of RF Institute of Mathematics and Computer Science... more Invitation
Ministry of Education and Science of RF
Institute of Mathematics and Computer Science
Siberian Federal University
XX
Conference
FINANCIAL and ACTUARIAL MATHEMTAICS
EVENTOLOGY of MULTIVARIATE STATISTICS
VI
Workshop
EVENTOLOGY of EXPERIENCE and CHANCE
HILBERT’s SIXTH PROBLEM
FAMEMS∼EEC∼H’s6P’2021
17 December 2021, Krasnoyarsk
FAMEMS’2021 ∼ Conference:
Themes of the FAMEMS include following directions, but are not limited by them exclusively. Any works with original
ideas are welcomed which induce application of mathematical and eventological methods in the most various areas.
Financial and actuarial mathematics
Mathematics in the humanities, socio-economic and natural sciences
Probability theory and statistics
Multivariate statistical analysis
Eventology of multivariate statistics
Co∼eventum mechanics
Theory of experience and chance
Eventology of safety
Eventology of risk and decision-making under risk and uncertainty
Philosophy of probability and event
Eventological economics and psychology
Eventological problems of artificial intelligence
Eventological aspects of quantum mechanics information theory
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∼H’s6P’2021 ∼ 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 co∼eventum mechanics and mathematical theories of experience and chance.
Topics of discussion include the results, thoughts and ideas on 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
Important dates:
November∼December 2021 — deadline for papers, and sessions
Instructions:
http://fam.conf.sfu-kras.ru/submission-e.php
Proceedings of the XVIII FAMEMS’2019 Conference, Part 1:
https://www.academia.edu/62707163/
Proceedings of the XVIII FAMEMS’2019 Conference, Part 2:
https://www.academia.edu/43861381/
Proceedings of the XIX FAMEMS’2020 Conference:
https://www.academia.edu/62731634/
Set functions and their summation are briefly considered in one important special case when the s... more Set functions and their summation are briefly considered in one important special case when the sets are the sets of Kolmogorov events [1-4].
Proceedings of the FAMEMs-2020 Conference, Krasnoyarsk, SFU Press, 2020
Set functions and their summation are briefly considered in one important special case when the s... more Set functions and their summation are briefly considered in one important special case when the sets are the sets of Kolmogorov events [1].
Möbius inversion formulas for the event-probability distributions of a set of events [1] are cons... more Möbius inversion formulas for the event-probability distributions of a set of events [1] are considered.
Proceedings of the XIII FAMEMS-2014 Conference, Krasnoyarsk, Siberian Federal University Press., 2014
We consider the notion of set-distance of NNN-set of events, characterizing an inconsistency of i... more We consider the notion of set-distance of NNN-set of events, characterizing an inconsistency of its events, and its extension up to an (N+1)(N+1)(N+1)-family of set-distances of different orders which are called set-distograms, characterizes the distribution of inconsistency of events relative to the power of subsets of the given set of events and serves as a convenient tool for detailed measurement of the inconsistency of a set of events.
Examples of set-distograms for several types of event-probability distributions of sets of events with different structures of consistency and inconsistency are given.
Attention is drawn to the fact that all three characteristics of an event: entropy, information, ... more Attention is drawn to the fact that all three characteristics of an event: entropy, information, and probability, depend on the observer of this event in the phenomenological sense, and not only because of the statistical errors of observation.
Keywords: Probability, entropy, information, observer, observation, Bertrand’s paradox, quantum contextuality.
Here an improved generalization of Feynman's paradox of negative probabilities [1, 2] for observi... more Here an improved generalization of Feynman's paradox of negative probabilities [1, 2] for observing three events is considered. This version of the paradox is directly related to the theory of quantum computing. Imagine a triangular room with three windows (see Fig. 1), where there are three chairs, on each of which a person can seat [3]. In any of the windows, an observer can see only the corresponding pair of chairs. It is known that if the observer looks at a window (to make a pair observation), the picture will be in the probabilistic sense the same for all windows: only one chair from the observed pair is occupied with a probability of 1/2, and there are never busy or free both chairs at once. Paradoxically, existing theories based on Kolmogorov's probability theory do not answer the question that naturally arises after such pairs of observations of three events: "What is really happening in a triangular room, how many people are there and with what is the probability distribution they are sitting on three chairs?". See also a random variable approach in [4, N.N.Vorob'ev, 1962].
The Rashomon effect occurs when an event is given contradictory interpretations by the individual... more The Rashomon effect occurs when an event is given contradictory interpretations by the individuals involved. The effect is named after Akira Kurosawa's 1950 film Rashomon, in which a murder is described in four contradictory ways by four witnesses [1]. The term addresses the motives, mechanism and occurrences of the reporting on the circumstance and addresses contested interpretations of events, the existence of disagreements regarding the evidence of events and subjectivity versus objectivity in human perception, memory and reporting. Lurking behind the theory of experience and chance, co∼eventum mechanics [2, 3, 4], and our modern understanding of mind and matter is the simple idea of co∼event. And among scientists, there is growing confidence that focusing on a co∼event is becoming more and more productive than it once was. Here we consider the co∼eventum mechanistic approach with the co∼eventum mechanistic Bayesian theorems [5] to analyze the Rashomon case in forensics.
For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it... more For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼ventum mechanics in the most approachable way. The main objective of co∼eventum mechanics and eventology [1] is the penetration of a new event-based language into all scientific and technological spheres and the development of the ability of the eventological potential of science and technology to transform the objects of study by event-based way, the formation of an interdisciplinary eventological paradigm that unifies, in the first place, socio-humanitarian, ecological, psycho-economic and other spheres, where scientific and technological research is difficult to imagine without including the observer in the subject of research, as well as the natural sciences in which the understanding of the impossibility of completely separating the subject of research from the observer has long been maturing. This is what I'm trying to do in this work. You yourself, or what is the same, your experience is such "coin" that, while you aren't questioned, it rotates all the time in "free light". And only when you answer the question the "coin" falls on one of the sides: "Yes" or "No" with the believability that your experience tells you.
Proceedings of the XIX FAMEMS'2020 Conference and the V Workshop on Hilbert's Sixth Problem, Krasnoyarsk: SFU, 2020
The theory of symmetric events, which was first published in [1] and which turned out to be usefu... more The theory of symmetric events, which was first published in [1] and which turned out to be useful in studying the relationship between eventological theory [2] and probability theory, is presented from the modern eventological point of view.
The dependence in modern directions of the theory of probability is the dependence, first of all, between random variables, i.e. between one-variate distribution functions.
It is quite clear that this dependence is generated by the dependence between the events on which the random variables are determined. The theory of symmetric events allows us to study in detail at the event level not only this dependence, which is traditionally studied in probability theory but also opens up a new opportunity to study how the form of each one-variate distribution function is determined by the structure of the dependencies of the set of symmetric events that determines this one-variate distribution function.
The fact is that in the theory of symmetric events each set of symmetric events has its own upper indicator, which is a pseudo-inverse function of the one-variate distribution function of this indicator.
Thus, the upper indicator of each set of symmetric events defines some one-variate distribution function.
This theory also shows that the range of different structures of dependencies of symmetric events is so wide that it covers the entire range of different types of one-variate distribution functions, which is determined by five reference distribution functions: from a degenerate distribution through binomial, equiprobable, and anti-binomial (this is a completely new distribution function that has yet to be studied in detail). to the distribution of a Boolean random variable. In this case, the degenerate distribution is determined by the set of least intersecting symmetric events, the binomial distribution is determined by the set of independent events, the equiprobable distribution is determined by the set of symmetric events with a pseudo-equiprobable distribution, the anti-binomial distribution is determined by the set of anti-independent symmetric events, and the Boolean distribution - by a set of nested coincident symmetric events.
So, the set of symmetric events is a convenient and widely applicable model for studying the types of one-variate distribution functions and how these types are determined by the structure of dependencies of a given set of symmetric events. Moreover, to study the types of two-variate and multivariate distribution functions, generalized event models from two or more sets of symmetric events are suitable under the assumption that their union is also a set of symmetric events.
Thus, as it turned out if one set of symmetric events determines the form of a one-variate distribution function, then two or more sets of symmetric events determine two-variate and multivariate distribution functions. In other words, the dependencies between one-variate distribution functions are determined, i.e. determine what is determined by the copula in modern probability theory.
Consequently, the sets of symmetric events and their structure of dependencies are suitable both for modeling copula (a well-studied direction in modern probability theory), which determine multivariate distribution functions for given one-variate and for modeling types of one-variate distribution functions, which is a completely new direction that is missing in modern probability theory.
Proceedings of the XI International FAMES'2012 Conference. Oleg Vorobyev, ed. - Krasnoyarsk: SFU. - 423 p., 2012
An eventological model of a mean-probable event for a set of events is proposed, which has analog... more An eventological model of a mean-probable event for a set of events is proposed, which has analogies with the concept of a mean-measure set that we introduced earlier.
(see also in English https://www.academia.edu/2328936/)
Proc. of the XV Intern. FAMEMS-2016 Conf. on Financial and Actuarial Math and Eventology of Multivariate Statistics, Krasnoyarsk, SFU (Oleg Vorobyev ed.), 44-93, 2016
This work is the third, but not the last, in the cycle begun by the works \cite{Vorobyev2016famem... more This work is the third, but not the last, in the cycle begun by the works \cite{Vorobyev2016famems1, Vorobyev2016famems2} about the new
theory of experience and chance as the theory of co~events. Here I introduce the concepts of two co~event means, which serve as dual co~event characteristics of some co~event. The very idea of dual co~event means has become the development of two concepts: mean-measure set \cite{Vorobyev1984} and mean-probable event \cite{Vorobyev2012fames4, Vorobyev2013sfu}, which were first introduced as two independent characteristics of the set of events, so that then, within the framework of the theory of experience and chance, the idea can finally get the opportunity to appear as two dual faces of the same co~event. I must admit that, precisely, this idea, hopelessly long and lonely stood at the sources of an indecently long string of guesses and insights, did not tire of looming, beckoning to the new co~event description of the dual nature of uncertainty, which I called the theory of experience and chance or the certainty theory. The constructive final push to the idea of dual co~event means has become two surprisingly suitable examples, with which I was fortunate to get acquainted in 2015, each of which is based on the statistics of the experienced-random experiment in the form of a co~event.
Eventology, theory of experience and chance, event, co~event, experience, chance, to happen, to experience, to occur, probability, believability, mean-believable (mean-experienced) terraced bra-event, mean-probable (mean-possible) ket-event, mean-believable-probability (mean-experienced-possible) co~event, experienced-random experiment, dual event means, dual co~event means, bra-means, ket-means, Bayesian analysis, approval voting, forest approval voting.
Proceedings of the XVII Conference on FAMEMS and the III Workshop on Hilbert's sixth problem. Krasnoyarsk, SFU, 44-53, 2018
We live in the real world, at such a time and in such circumstances, when not only principles bu... more We live in the real world, at such a time and in such circumstances, when not only principles but also facts blur, become overgrown with lies and pretense. The endless cycle of our indefinite co∼being forces observers to look for tools capable of coping with the challenges of uncertainty world, which would make it possible to comprehend, express and measure vague principles, facts, lies, and pretense. However, note that we have always lived, we live and we will live in the world of co∼events which is mathematically controlled by the theory of experience and chance and the co∼eventum mechanics. The main tools of these new theories are two measures: probabilistic and believabilistic, which are intended to comprehend, express and measure our co∼eventum world. The probability measures the future chance of observation, the believability measures the past experience of an observer. This paper shows that these two measures are naturally related to each other in the co∼eventum mechanistic H-theorem, and this connection between the past uncertainty of experience and the future uncertainty of chance is expressed using the Gibbs distribution, which is based on the extreme entropy conditions.
A co∼eventum mechanistic generalization of the eventological H-theorem is proposed, which determines the extreme-entropy properties of Gibbs distributions in the co∼eventum mechanics where Gibbs distributions relate the past experience of observers with the future chance of observations. The co∼eventum mechanistic H-theorem, a co∼eventum generalization of the Boltzmann H-theorem from statistical mechanics, justifies the application of Gibbs distributions of co∼events minimizing relative entropy, as statistical models of the behavior of a rational subject, striving for an equilibrium co∼eventum choice between the past experience and the future chance in various spheres of her/his co∼being.
Fréchet bounds of the 1st kind for sets of events and their main properties are considered in mor... more Fréchet bounds of the 1st kind for sets of events and their main properties are considered in more detail than in [1]. The theorem on not more than two nonzero values of lower Fréchet-bounds of the 1st kind for a set of half-rare events is proved with the corollary on the analogous assertion for sets of events with arbitrary event-probability distributions.
Keywords: probability, event, set of events, event-probability distribution, set of half-rare events, Fréchet bounds of the 1st kind.
Proceedings of the FAM-2008 Conference, Krasnoyarsk, Siberian Federal University Press, 2008
A thorough introduction to the theory of multicovariance of events is given, the beginnings of wh... more A thorough introduction to the theory of multicovariance of events is given, the beginnings of which are fragmentarily presented in [https://www.academia.edu/38605343, https://www.academia.edu/189393].
A multicovariance is a multiplicative version of the measure of the dependence of events and serves as a convenient tool for analyzing the structures of event dependencies, successfully complementing the traditional additive variant of the measure of the dependence of events, a covariance.
The theory of multicovariances of events is indispensable in the study of the classes of Gibbs and anti-Gibbs eventological distributions that associate probability with the entropy, information and value of events; as well as in the analysis and solution of the variational problems of the eventological information theory, in which they look for the equilibrium eventological distributions of the sets of events, providing an extreme of entropy or relative entropy under various kinds of restrictions on certain subsets of events.
In addition, the eventological multicovariance theory is effectively used in numerous eventology applications for modeling humanitarian and socioeconomic systems.
The Rashomon effect occurs when an event is given contradictory interpretations by the individual... more The Rashomon effect occurs when an event is given contradictory interpretations by the individuals involved. The effect is named after Akira Kurosawa's 1950 film Rashomon, in which a murder is described in four contradictory ways by four witnesses [1]. The term addresses the motives, mechanism, and occurrences of the reporting on the circumstance and addresses contested interpretations of events, the existence of disagreements regarding the evidence of events, and subjectivity versus objectivity in human perception, memory, and reporting. Lurking behind the theory of experience and chance, co∼eventum mechanics [2, 3, 4], and our modern understanding of mind and matter is the simple idea of co∼event. And among scientists, there is growing confidence that focusing on a co∼event is becoming more and more productive than it once was. Here we consider the co∼eventum mechanistic approach with the co∼eventum mechanistic Bayesian theorems [5] to analyze the Rashomon case in forensics.
Proceedings of the XX FAMEMS 2021 Conference VI H’s6P Workshop, 80pp, Krasnoyarsk, SFU Press, 2021
C o n t e n t s Boucon Jean-Louis (France) Hilbert’s project and the transcendental Blaszyn... more C o n t e n t s
Boucon Jean-Louis (France)
Hilbert’s project and the transcendental
Blaszynski John and Trevor Blaszynski (Hamilton, Canada)
Spring Theory: Life Before and During the Big Bangs
Richfield Jon (Stellenbosch, Western Cape, South Africa )
Hilbert-6 — An Uninformed Reaction
Richfield Jon (Stellenbosch, Western Cape, South Africa )
Hilbert’s 6th problem, Plesiomorphism, and Meta-axiomatics
Urban Roman (Wroclaw, Poland)
On interrelation between conceptual spaces, opinion dynamics, and eventology theory
Vorobyev Oleg (Krasnoyarsk, Russia)
Multivariate discrete distributions, multivariate copulas, and event-probability distributions
Proceedings of the XIX FAMEMS'2020 Conference and the V Workshop on Hilbert's Sixth Problem, Krasnoyarsk: SFU, 2020
C o n t e n t Baranova Irina (Krasnoyarsk) Sets of bipartite events sets and applications Blasz... more C o n t e n t
Baranova Irina (Krasnoyarsk)
Sets of bipartite events sets and applications
Blaszynski John (Hamilton, Canada)
DSM Predicts Invisible Matter and the Standard Model at Big Bang
Blaszynski John and Trevor Blaszynski (Hamilton, Canada)
DSM Predictions of a Multi-Bang Universe, Higgs Boson and Leaping Leptons
Gilin Stepan (Krasnoyarsk)
Application of neural networks and the hidden Markov models
to the solution of the problem words recognition in audio records
Vorobyev Oleg (Krasnoyarsk)
The theory of a set of symmetric events
Vorobyev Oleg (Krasnoyarsk)
The main formulas of a set summation
Vorobyev Oleg (Krasnoyarsk)
Entropy, information, and probability of events
phenomenologically depend on an observer
Vorobyev Oleg (Krasnoyarsk)
Möbius inversion formulas
for the event-probability distributions of a set of events
Proceedings of the XVIII FAMEMS'2019 Conference and the IV Workshop on Hilbert's Sixth Problem, Krasnoyarsk: SFU. Part 1: 1-127pp., 2019
C o n t e n t s Poddubny Vasil (Tomsk) Analysis of the Influence of Errors in the Values of Att... more C o n t e n t s
Poddubny Vasil (Tomsk)
Analysis of the Influence of Errors in the Values of Attributes
of Binary Objects on the Quality of their Recognition
Soiguine Alexander (Aliso Viejo, CA USA)
Lift of Complex Analysis in Terms of Geometric Algebra
Kustitskaya Tatiana (Krasnoyarsk)
Statistical analysis of the existence of debt claims for a credit portfolio
Baranova Irina (Krasnoyarsk)
Applications of sets of bipartite sets of events
Blaszynski John and Trevor Blaszynski (Hamilton, Canada)
Then there was 𝐻. A History of the Universe. This is Her story
Gilin Stepan and Irina Baranova (Krasnoyarsk)
Solution of the problem of word recognition in audio records with using of neural networks and Hidden Markov Models
Jean Catherine MacPhail (United Kingdom)
Complementarity within two examples of the invariance principle in vertical models of consciousness
Vorobyev Oleg (Krasnoyarsk)
The axiom of experience vs the axiom of chance in the theory of experience and chance
Vorobyev Oleg (Krasnoyarsk)
Two different dual types of statistical dependencies:
the ket-dependence of observations and the bra-dependence of observers
Vorobyev Oleg (Krasnoyarsk)
The event-based studying the statistical dependency structure of a co∼event
Vorobyev Oleg (Krasnoyarsk)
Eigen-distribution and fixed-distributions of a co∼event, and the new Bayesian schemes in the theory of experience and chance
Vorobyev Oleg (Krasnoyarsk)
Two levels of fuzziness in the theory of co∼events
Vorobyev Oleg (Krasnoyarsk)
Probability and believability distributions of a co∼event that defined by the five new co∼event-based Bayesian theorems
Vorobyev Oleg (Krasnoyarsk)
How probability theory differs from measure theory
Proceedings of the XVIII FAMEMS'2019 Conference and the IV Workshop on Hilbert's Sixth Problem, Krasnoyarsk: SFU., 2019
C o n t e n t s Poddubny Vasil (Tomsk) Analysis of the Influence of Errors in the Values of Att... more C o n t e n t s
Poddubny Vasil (Tomsk)
Analysis of the Influence of Errors in the Values of Attributes
of Binary Objects on the Quality of their Recognition
Soiguine Alexander (Aliso Viejo, CA USA)
Lift of Complex Analysis in Terms of Geometric Algebra
Kustitskaya Tatiana (Krasnoyarsk)
Statistical analysis of the existence of debt claims for a credit portfolio
Baranova Irina (Krasnoyarsk)
Applications of sets of bipartite sets of events
Blaszynski John and Trevor Blaszynski (Hamilton, Canada)
Then there was 𝐻. A History of the Universe. This is Her story
Gilin Stepan and Irina Baranova (Krasnoyarsk)
Solution of the problem of word recognition in audio records with using of neural networks and Hidden Markov Models
Jean Catherine MacPhail (United Kingdom)
Complementarity within two examples of the invariance principle in vertical models of consciousness
Vorobyev Oleg (Krasnoyarsk)
The axiom of experience vs the axiom of chance in the theory of experience and chance
Vorobyev Oleg (Krasnoyarsk)
Two different dual types of statistical dependencies:
the ket-dependence of observations and the bra-dependence of observers
Vorobyev Oleg (Krasnoyarsk)
The event-based studying the statistical dependency structure of a co∼event
Vorobyev Oleg (Krasnoyarsk)
Eigen-distribution and fixed-distributions of a co∼event, and the new Bayesian schemes in the theory of experience and chance
Vorobyev Oleg (Krasnoyarsk)
Two levels of fuzziness in the theory of co∼events
Vorobyev Oleg (Krasnoyarsk)
Probability and believability distributions of a co∼event that defined by the five new co∼event-based Bayesian theorems
Vorobyev Oleg (Krasnoyarsk)
How probability theory differs from measure theory
Proceedings of the XVII FAMEMS'2018 Conference and the III Workshop on Hilbert's Sixth Problem, Krasnoyarsk, SFU, 169p, ISBN-978-5-9903358-8-2.
Financial and actuarial mathematics Mathematics in the humanities, socio-economic and natural sci... more Financial and actuarial mathematics
Mathematics in the humanities, socio-economic and natural sciences
Probability theory and statistics
Multivariate statistical analysis
Eventology of multivariate statistics
Co~eventum mechanics
Theory of experience and chance
Eventology of safety
Eventology of risk and decision-making under risk and uncertainty
Philosophy of probability and event
Eventological economics and psychology
Eventological problems of artificial intelligence
Eventological aspects of quantum mechanics information theory
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
Proceedings of the XVII FAMEMS'2018 Conference and the III Workshop on Hilbert's Sixth Problem, Krasnoyarsk, SFU, 169p, ISBN-978-5-9903358-8-2., 2018
Financial and actuarial mathematics Mathematics in the humanities, socio-economic and natural sci... more Financial and actuarial mathematics
Mathematics in the humanities, socio-economic and natural sciences
Probability theory and statistics
Multivariate statistical analysis
Eventology of multivariate statistics
Co~eventum mechanics
Theory of experience and chance
Eventology of safety
Eventology of risk and decision-making under risk and uncertainty
Philosophy of probability and event
Eventological economics and psychology
Eventological problems of artificial intelligence
Eventological aspects of quantum mechanics information theory
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
Proceedings of the XVI FAMEMS'2017 Conference and the II Hilbert's Sixth Problem Workshop, Krasnoyarsk, SFU, 162p., 2018
Eventology of multivariate statistics Eventology and mathematical eventology Philosophical evento... more 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 axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem.
Eventology of experience and chance
Beleivability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance
Eventology of multivariate statistics Eventology and mathematical eventology Philosophical evento... more 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 multivariate statistics Eventology and mathematical eventology Philosophical evento... more 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
Eventology of multivariate statistics Eventology and mathematical eventology Philosophical evento... more 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
Proc. of the XIII Conference on Financial and Actuarial Math and Eventology of Multivariate Statistics, 251pp., Apr 19, 2014
Financial and actuarial mathematics Eventology of multivariate ststistics Eventology of safety ... more 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
Proceedings of the XII FAMES 2013 Conference on Financial and Actuarial Maths and Eventology of Safety, Apr 21, 2013
Financial and actuarial mathematics Eventology of multivariate ststistics Eventology of safety Ev... more 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
Proceedings of the XVI EM 2012 Conference on Eventological Math, Dec 2012
en.scientificcommons.org
The development of probability theory together with the Bayesian approach in the three last centu... more 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 ...
A new approach to portfolio analysis of financial market risks by random set tools is considered.... more A new approach to portfolio analysis of financial market risks by random set tools is considered. Despite many attempts, the consistent and global modeling of financial markets remains an open problem. In particular it remains a challenge to find a simple and tractable economic and probabilistic approach to market modeling. This paper attempts to highlight fundamental properties that a market
Proceedings of the XIII FAMEMS-2014 Conference, Krasnoyarsk, Siberian Federal University Press., Apr 19, 2014
We consider the notion of set-distance of NNN-set of events, characterizing an inconsistency of ... more We consider the notion of set-distance of NNN-set of events, characterizing an inconsistency of its events, and its extension up to an (N+1)(N+1)(N+1)-family of set-distances of different orders which are called set-distograms, characterizes the distribution of inconsistency of events relative to the power of subsets of the given set of events and serves as a convenient tool for detailed measurement of the inconsistency of a set of events.
Examples of set-distograms for several types of event-probability distributions of sets of events with different structures of consistency and inconsistency are given.
Eprint Arxiv 0811 0420, Nov 4, 2008
The eventological theory of decision-making, the theory of eventfull decision-making is a theory ... more The eventological theory of decision-making, the theory of eventfull decision-making is a theory of decision-making based on eventological principles and using results of mathematical eventology; a theoretical basis of the practical eventology. The beginnings of this theory which have arisen from eventfull representation of the reasonable subject and his decisions in the form of eventological distributions (E-distributions) of sets of events and which are based on the eventological H-theorem are offered. The illustrative example of the eventological decision-making by the reasonable subject on his own eventfull behaviour in the financial or share market is considered.
Remaking the primary source of an old good idea of the “lattice expectation”, published by me in ... more Remaking the primary source of an old good idea of the “lattice expectation”, published by me in 1975 at the first time and subsequently, especially in the western literature on stochastic geometry and the theory of random sets, named from a light hand of Dietrich Stoyan [1994] “Vorob’ev expectation”; had an only historical and methodic value for eventology and probability theory once more reminding how and “...from what rubbish flowers grow, not knowing shame”.
An eventologiсal glance at the generalization of the concept of Fr'echet bounds for the proba... more An eventologiсal glance at the generalization of the concept of Fr'echet bounds for the probability of arbitrary set-theoretic operation on a finite set of c'o-events is proposed.
Choice Reviews Online, 1998
The development of probability theory together with the Bayesian approach in the three last centu... more 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 phenom- ena and partial ignorance about them. As now it is standard to believe (1), the nature of these key factors is so various, that their descriptions are required special uncer- tainty theories, which difier from the probability theory and the Bayesian credo, and provide a better account of the various facets of uncertainty by putting together prob- abilistic and set-valued representations of information to catch a distinction between variability and ignorance. Eventology (2), a new direction of probability theory and philosophy, ofiers the original event approach to the description of variability and ig- norance, entering an agent, together with his/her beliefs, directly in the frameworks of scientiflc research in the form of eventological distribution of his/her own events. This allows eventology, by putting together p...
The main theorem of the games theory of random coalitions is reformulated in the random set langu... more The main theorem of the games theory of random coalitions is reformulated in the random set language which generalizes the classical maximin theorem but unlike it defines a coalition imputation also. The theorem about maximin random coalitions has been introduced as a ...
Some believe that probability theory is a special case of measure theory. Others say that probabi... more Some believe that probability theory is a special case of measure theory. Others say that probability theory is distinguished from measure theory by the notion of independence of events. Both are right and wrong in their own right. This work points to the axiomatic difference between these theories, which became quite obvious in connection with the axiomatization of the new theory of experience and chance [1]. This new theory is a synthesis of two dual theories: probability theory and believability theory, each of which narrows measure theory by adding one axiom to it. Probability theory adds the axiom of chance to the axioms of measure theory, and the theory of believability adds the axiom of experience. Namely, it is these additional axioms that both theories differ from measure theory.
If in order to solve a problem you need a capacity or a non-additive measure or even a fuzzy meas... more If in order to solve a problem you need a capacity or a non-additive measure or even a fuzzy measure, than it does not mean that the problem does not fit into Kolmogorov's probability theory. It just means that trying to solve the problem at hand you deal not with events, but with sets of events, and you talk about non-additivity of a function of these sets (set-function), which you call a capacity or a fuzzy measure. But then again you assume that both a capacity and a fuzzy measure are an extension of probability. Now this actually goes beyond Kolmogorov's probability theory (ha!) to the realm, where its additive foot has never trodden. The point is that you are using not events (which, let's face it, you often choose to forget in much simpler situations, but still have to recall inaptly in slightly more complex situations), but - sets of events, though you are still certain that you are using events. Of course, your set-function is non-additive in its argument, which is a set of events - a subset of algebra A, but not an event --- a subset of Omega. This non-additive set-function is generated by a probability measure (yes, the additive Kolmogorov's one) of terrace events, which are just bijectively ``indexed'' by sets of events. All of these allegedly non-additive extensions of probability are flesh of its flesh generations. They cannot even stir a step without supreme orders from Her Royal Additivity - probabilities are governed, down to the smallest detail, and at her pleasure they may become additive, k-additive, totally monotonous, or k-monotonous in turn. Her Royal Additivity rules the day in this world and meticulously imposes non-additive features, every single one of them, on capacities and fuzzy measures.
It is usually said that probability theory is a theory that calculates the probabilities of some ... more It is usually said that probability theory is a theory that calculates the probabilities of some events through the probabilities of other events. But this, as a rule, the correct denition not only can be misleading but has already been misleading for a long time. Because it overlooks the very important notion of a probability distribution of a set of events, an event-probability distribution (e-p.d.). The set of events (s.e.) serves as the central concept of that part of probability theory, which can be called the science of events, eventology [1]. Therefore the fact is that it is more correct to say that probability theory calculates the probability distributions of some sets of events through the probability distributions of other sets of events. The topics of my articles are only parts of the direction in probability theory, which can be called the theory of events, or eventological theory. The most important problem in the theory of sets of events is the description of the classes of e-p.d's of sets of events that have given probabilities of events. The fact is that such classes differ only in the structures of probabilistic dependencies between events. A detailed description of such classes is the most important task of both the theory of sets of events and the theory of probability in general 1. To some, such a statement may seem too strong, especially in relation to the probability theory in general. However, if you remember that the distribution function of a multivariate random vector is dened as the probability of intersection of sets of events numbered with the values of this random vector, then everything will fall into place. The modern theory of probability, the one that is used with great success in numerous applications, can be called without special stretch the theory of random variables, random vectors, random functions, etc. In other words, the theory of one whose domain of denition is always a set of events. Namely, a set of events with their structure of probability dependencies controls random variables, and random vectors, and random functions, and other constructions with an event space as a domain of denition. Therefore, in my opinion, the theory of sets of events and their structures of probability dependencies is or should be one of the main directions of modern probability theory. I think it is unnecessary to give concrete examples of this. Such examples are not only many, but very many. We tested, for example, portfolio theory of events [6], [7], event models of the supply and demand market [8], eventological theory of decision-making [9], and Bayesian event analysis [10], from the point of view of event theory. And in each of these areas new interesting results were obtained. Thus, I have every reason to state that the eventological theory stimulates new insights in mathematics, answers questions from other elds, and solves problems in real-world applications. But even if I am mistaken in the rst as well as in the second and third cases, the eventological theory in which many beautiful results are proved will remain important in itself, however, like all mathematics, which is basically useless for any practical use. You can ask a reasonable question: «How is the eventological theory useful at all in any application?» In whatever area of real-world applications you have to conduct your research, you will encounter some statistics of observations of one or another set of events. And if you know the statement of some event theorem, then it should be clear to you that the set of events has some properties under some conditions. Such seemingly abstract knowledge, which in real applications is interpreted in terms of this application, is usually more than useful. Also we can say that the theorem of this paper is just a clear example of the fact that the study of the dependence structure of an arbitrary set of events can always be reduced to the study of the dependence structure of its half-rare projection by applying the corresponding set-phenomenal renumbering of probabilities from its distribution (see [11]). However, besides this, it turns out that the theory of the so-called eventological copula (Kopula) [2] is based on the set-phenomenal renumbering method that was used to prove this theorem. Everyone knows that in the theory of copula (see [12] for example), Sklar's theorem [13] states that any multivariate joint distribution can be written in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables. My similar theorem [2] under substantially less restrictive assumptions states that any e-p.d. of a set of events can be written in terms of probabilities of its events and an eventological copula (Kopula) which describes the dependence structure between the events. To my deep regret, while in the paper I am forced to refer mainly only to my articles. But the explanation lies on the surface: few people know the eventological theory. Eventology and its applications are at the beginning of their formation.
In our papers [1] and [2], great and little co∼event-based Bayesian theorems were proved. Here we... more In our papers [1] and [2], great and little co∼event-based Bayesian theorems were proved. Here we reformulate these theorems and also formulate a new co∼event-based Bayesian theorem just to describe how all these Bayesian-wise theorems transform the probabilistic and believabilistic distributions of a co∼event. In other words, how these theorems transform the spaces of probability and believability co∼event distributions.
The co∼event theory [1] allows you to distinguish between two levels of what is commonly called f... more The co∼event theory [1] allows you to distinguish between two levels of what is commonly called fuzziness in modern fuzzy mathematics. This is the fuzziness that Zadeh [2, 3], the creator of the theory of fuzzy sets, had in mind. Moreover, the one level of fuzziness, which usually serves as the subject of study of modern fuzzy mathematics, is studied by one of the dual halves of the co∼event theory: the believability theory and another level of fuzziness is the subject of research of the co∼event theory as such. In this work, we strictly dene both levels of fuzziness, examine their properties, relationships, differences, and interpretations in practical applications. The external level of fuzziness characterizes a co∼event (as a measurable binary relation) that is a result of an experienced-random experiment, the internal level characterizes a fuzzy co∼event (as a measurable fuzzy binary relation) that is a result of a fuzzy experienced-random experiment. The external level of fuzziness is generated by differences in the experience of the set of observers who participate in the experienced random experiment. The internal level of fuzziness is generated by instabilities in the experience of each observer who participate in the experienced random experiment. The fuzziness of the external level is only a redefinition of the generally accepted concept of fuzziness within the framework of the co∼event theory.
Our recently introduced theory of experience and chance, intended for the axiomatic description o... more Our recently introduced theory of experience and chance, intended for the axiomatic description of the well-known conflict between observers and observations, clearly indicated that in our quantum world, in addition to the statistical dependencies of the so-called ket-events that are controlled by probability and measured, for example, by the Pearson correlation coefficient, there are statistical dependencies of the so-called bra-events that are controlled by the dual measure, believability.
In this work, we finally managed to deal with these dual statistical dependencies and give a rigorous definition of the statistical ket-dependence, which coincides with the usual definition of the probability dependence of Kolmogorov events, and a new statistical bra-dependence, which turned out to be a distant analogy of that well-known statistical dependence which is measured by Kendall's tau.
Now, relatively little attention has been paid on the interrelations between Pearson's rrr and Kendall's tau\tautau under the different random variable models. We intentionally do not give a review of such works, because they can add little and are unlikely to clarify the new co$\sim$event-based approach to the analysis of statistical correlations that is proposed in our work.
Our goal in this article is to analyze the event basics of modern correlation theory using the example of these two most popular measures of statistical dependence
which are interpreted in the theory of experience and chance as two dual statistical dependencies. The first of these is the statistical dependence between observations, the second is the statistical dependence between observers.
It is no secret that modern correlation theory is oriented primarily and mainly to the study of statistical dependencies between random variables.
However, random variables are nothing but measurable functions defined on the space of events.
Namely, the dual structure of statistical dependencies of the sets of ket-events and bra-events on which those or other random or experienced variables are determined completely determines the dual structure of statistical dependencies between them.
This paper studies the interrelations between the very well-known Kendall's tau and Pearson correlation coefficient
at the multivariate case in the framework of the co$\sim$event-based theory of experience and chance.
In other words, in this paper, we are going to compare these correlation coefficients at a primitive co$\sim$event-based level, where we measure not the correlation of arbitrary random variables, but the correlation of ket-events and bra-events, or, if you want, the correlation of Bernoulli random and experienced ket-variables and bra-variables.
For many years already, the eventological theory has used such measures of the statistical dependence of a set of events as the Fr\'echet correlation and the event analog of the Pearson correlation coefficient.
In this work, for the first time, we also introduce co$\sim$event-based analog of Kendall's tau and another new analog of the Pearson correlation coefficient.
We find that the interesting interrelations between these measures of statistical dependencies of ket-events and bra-events, for example, between Pearson rrr and Kendall tau\tautau. Moreover, the theorem (see Theorem 1) is proved which states that the inequality, −1/3leqslanttauxyzleqslant1-1/3\leqslant \tau_{xyz} \leqslant 1−1/3leqslanttauxyzleqslant1 for the triplet of events x,y,z\{x,y,z\}x,y,z, and also more general inequalities for tauX\tau_XtauX at a multivariate case where XXX is a set of events, are true. Also, the sets of events are indicated at which Kendall's tau takes the lowest possible values (see Theorem 2).
Also using elegant dualism between definitions of Pearson correlation coefficient and Kendall's tau for a doublet of ket-events and bra-events, we give the new definition of Pearson correlation coefficient for a set of ket-events, i.e., at a multivariate case.
The co$\sim$event-based theory of experience and chance \cite{Vorobyev2016famems2} gives us an always new unexpected and fruitful point of view on any problem that arises as a result of the conflict between observers and observations.
Only experience and chance rule our world.
I invite you to this territory of ours, which, although it can never get rid of the yoke of experience and chance, lives according to the laws adopted by the new axiomatics of past experience and the dual Kolmogorov axiomatics of the future chance.
As recently discovered, this two dual axiomatics define two types of dependencies in our territory: the bra-dependence of past experiences and the ket-dependence of future chances.
Today, we will be able to build a portrait of our territory in the phase spaces of these two dual statistical dependencies.
The author hopes that this study of the dual structure of the statistical dependencies of a set of ket-events and bra-events, firstly, contributes to the further development of both the eventological theory \cite{Vorobyev2007} and the theory of experience and chance \cite{Vorobyev2016famems2}, and, secondly, it will help to clarify some problems of the modern correlation theory where the conflict between observers and observations is investigated.
We tested the very well-know statistical dependency indicators: Kendall's tau and Pearson's corre... more We tested the very well-know statistical dependency indicators: Kendall's tau and Pearson's correlation coecient, and the pair of new statistical event dependency indicators: Fréchet correlation and modied Pearson's correlation coecient, and compared their simplest properties in a series of intuitively transparent examples of evaluating the dependence of sets of events. The results for these problems are not very optimistic for the usual indicators, but look promising for newly introduced indicators. The indication of the statistical dependence of sets of events causes well-known and widely discussed problems in many applied elds, including, for example, the problem of Bell inequalities in quantum physics. We systematically test these indicators in a series of intuitively understandable examples. A systematic comparison shows that the difference between the old and new indicators is statistically signicant and clearly indicates the advantage of the new indicators.
As a result of an experimentally random experiment a co∼event serves. A co∼event is an axiomatica... more As a result of an experimentally random experiment a co∼event serves. A co∼event is an axiomatically based mathematical model of the interaction of observers and observations, which allows you to answer many, if not all, of the questions that usually arise in various fields and related to the «observer-observation» conflict. The co∼event is based on the theory of experience and chance [1], which contains the Kolmogorov probability theory as one of the dual halves. The other half is the theory of believability with believability measure. Believability measures the experience of the observer in the same way that probability measures the chance of observation.
Any elementary experience refers to the chance observed by it, that is, gives the name to the obs... more Any elementary experience refers to the chance observed by it, that is, gives the name to the observed chance, which is composed of many elementary observed chances. Simply put, the elementary experience of observing a chance itself is the name of this chance, that is, the name of the set of elementary observable chances that form it.
Our world is a world of observers and observations. Observers are a product of the experience giv... more Our world is a world of observers and observations. Observers are a product of the experience given to them in the past. Observations are products of chances that are provided by the future. This dualism of observers and observations is axiomatized in the new mathematical theory of experience and chance, or co∼eventum mechanics (see [2],[3]). The axiomatics of the theory of experience and chance is based on two main axioms: the Kolmogorov axiom of the future chance, on which the modern probability theory is built (theory of chance), and the axiom of the past experience, on which the dual reflection of probability theory is based-a new theory of believabilities (theory of experience). This pair of dual theories forms a theory of experience and chance, which in the very near future can give an axiomatized mathematical impulse to the solution of the long-standing problem of the axiomatization of physics (Hilbert's sixth problem). The current development of the theory of experience and chance gives quite encouraging results in various fields of a mathematical description of uncertainty and chaos. It is enough to point out fresh co∼eventum approaches in Bayesian analysis and statistical correlation theory. Today is a time when the efforts of a wide scientific community are required to deepen understanding and master a new co∼eventum outlook on the dual world of observers, burdened by past experience, and observations, pregnant with the future chance.
Fixed-distributions and eigen-distributions of a co∼event, and the new Bayesian theorem in the th... more Fixed-distributions and eigen-distributions of a co∼event, and the new Bayesian theorem in the theory of experience and chance.
Example. An experientially random experiment is conducted in which a group of M = 4 experienced experts (observers) ranks a random collection of N = 5 trees (observations) into two ranks: «to be cut» (×) or «not to be cut».
Proceedings of the XVIII FAMEMS Conference and IV H's6P Workshop, 2019
Our recently introduced theory of experience and chance, intended for the axiomatic description o... more Our recently introduced theory of experience and chance, intended for the axiomatic description of the well-known conflict between observers and observations, clearly indicated that in our quantum world, in addition to the statistical dependencies of the so-called ket-events that are controlled by probability and measured, for example, by the Pearson correlation coefficient, there are statistical dependencies of the so-called bra-events that are controlled by the dual measure, believability.
In this work, we finally managed to deal with these dual statistical dependencies and give a rigorous definition of the statistical ket-dependence, which coincides with the usual definition of the probability dependence of Kolmogorov events, and a new statistical bra-dependence, which turned out to be a distant analogy of that well-known statistical dependence which is measured by Kendall's tau.
Now, relatively little attention has been paid on the interrelations between Pearson's rrr and Kendall's tau\tautau under the different random variable models. We intentionally do not give a review of such works, because they can add little and are unlikely to clarify the new co$\sim$event-based approach to the analysis of statistical correlations that is proposed in our work.
Our goal in this article is to analyze the event basics of modern correlation theory using the example of these two most popular measures of statistical dependence
which are interpreted in the theory of experience and chance as two dual statistical dependencies. The first of these is the statistical dependence between observations, the second is the statistical dependence between observers.
It is no secret that modern correlation theory is oriented primarily and mainly to the study of statistical dependencies between random variables.
However, random variables are nothing but measurable functions defined on the space of events.
Namely, the dual structure of statistical dependencies of the sets of ket-events and bra-events on which those or other random or experienced variables are determined completely determines the dual structure of statistical dependencies between them.
This paper studies the interrelations between the very well-known Kendall's tau and Pearson correlation coefficient
at the multivariate case in the framework of the co$\sim$event-based theory of experience and chance.
In other words, in this paper, we are going to compare these correlation coefficients at a primitive co$\sim$event-based level, where we measure not the correlation of arbitrary random variables, but the correlation of ket-events and bra-events, or, if you want, the correlation of Bernoulli random and experienced ket-variables and bra-variables.
For many years already, the eventological theory has used such measures of the statistical dependence of a set of events as the Fr\'echet correlation and the event analog of the Pearson correlation coefficient.
In this work, for the first time, we also introduce co$\sim$event-based analog of Kendall's tau and another new analog of the Pearson correlation coefficient.
We find that the interesting interrelations between these measures of statistical dependencies of ket-events and bra-events, for example, between Pearson rrr and Kendall tau\tautau. Moreover, the theorem (see Theorem 1) is proved which states that the inequality, −1/3leqslanttauxyzleqslant1-1/3\leqslant \tau_{xyz} \leqslant 1−1/3leqslanttauxyzleqslant1 for the triplet of events x,y,z\{x,y,z\}x,y,z, and also more general inequalities for tauX\tau_XtauX at a multivariate case where XXX is a set of events, are true. Also, the sets of events are indicated at which Kendall's tau takes the lowest possible values (see Theorem 2).
Also using elegant dualism between definitions of Pearson correlation coefficient and Kendall's tau for a doublet of ket-events and bra-events, we give the new definition of Pearson correlation coefficient for a set of ket-events, i.e., at a multivariate case.
The co$\sim$event-based theory of experience and chance \cite{Vorobyev2016famems2} gives us an always new unexpected and fruitful point of view on any problem that arises as a result of the conflict between observers and observations.
Only experience and chance rule our world.
I invite you to this territory of ours, which, although it can never get rid of the yoke of experience and chance, lives according to the laws adopted by the new axiomatics of past experience and the dual Kolmogorov axiomatics of the future chance.
As recently discovered, this two dual axiomatics define two types of dependencies in our territory: the bra-dependence of past experiences and the ket-dependence of future chances.
Today, we will be able to build a portrait of our territory in the phase spaces of these two dual statistical dependencies.
The author hopes that this study of the dual structure of the statistical dependencies of a set of ket-events and bra-events, firstly, contributes to the further development of both the eventological theory \cite{Vorobyev2007} and the theory of experience and chance \cite{Vorobyev2016famems2}, and, secondly, it will help to clarify some problems of the modern correlation theory where the conflict between observers and observations is investigated.
We are doomed to live in a world of chaos. After all, we have to survive. Chaos is given to us be... more We are doomed to live in a world of chaos. After all, we have to survive. Chaos is given to us besides our will and entices us with two robes. This is either past experience or future chance. We perceive, feel, and recognize chaos in our past experience and our future chance. Little by little, we began to realize that the tools to survive in a world of chaos could be only our past experience and our future chance. Both the experience and the chance are generated by chaos, they are both chaotic. The chaotic state of the chance, we used to call randomness. But the chaotic state of the experience, we have not yet managed to call a stable philosophy word. There are no other synonyms to denote this property of experience, except for the trivial word «experience». So the chaotic state of experience is the experience. We firmly connect a future chance and a frequency. We are used to measuring a chance by its frequency. But frequency can also measure our past experience. Thus, frequency is a characteristic not only of future chance but also a characteristic of past experience. Therefore, on completely reasonable grounds, the frequency can be considered as an attribute of chaos. Usually, we talk about random numbers, when we associate them with the future chance, therefore there is no reason to keep silent about the experience numbers, linking them with past experience. In both cases, we are talking about chaotic numbers. In my opinion, if we want to analyze chaos from two dual points of view, chaotic numbers should be a general term for random numbers in the future chance and for experience numbers in the past experience. The theory of experience and chance [1], which I proposed to describe chaos, involves two dual logics of analysis of the future chance and the past experience. These dual logics rely on the new dual axiomatics, which includes the Kolmogorov axiomatics of probability theory, as one of the dual halves, and in which the dual axiom of the past experience is compared to the Kolmogorov axiom of the future chance [2].
This explains the fundamental difference between the two axioms. One of which, the axiom of chanc... more This explains the fundamental difference between the two axioms. One of which, the axiom of chance, was introduced by Kolmogorov with his axiomatization of the theory of probability, although he did not call it an axiom. The other, the axiom of experience, which plays a similar role in the dual theory of believability, is formulated in essentially different ways. To facilitate the perception of the meaning of this difference, as well as its far-reaching consequences, which relate to the concept of the past experience and the future chance, these axioms are accompanied by illustrations in the form of Venn diagrams.
Many of us have long been accustomed to the idea that we live to seek truth in a probabilistic wo... more Many of us have long been accustomed to the idea that we live to seek truth in a probabilistic world. We consider probability as a measure of truth. However, the leading founders of quantum mechanics agreed with Niels Bohr that, apart from truth, there is still clarity, which is dual to truth. Formulated by Bohr the complementarity principle holds that events have certain pairs of complementary properties which cannot all be observed or measured simultaneously. In [1, 2, 2016] I proposed a new theory, which I called the theory of experience and chance or the theory of co∼events, which includes probability theory as one of the dual parts. The theory of probability in this new theory complements what I called the theory of believability. The probability theory measures chances of observations, and the believability theory measures the experience of observers. So, one can also say we live to seek the truth of chance and the truth of experience in a probabilistic-believabilistic world. Experience and chance complement each other in full accordance with the general principle of complementarity. The mathematical model of such a pair is a co∼event, which is the central concept of the theory of experience and chance. The multi-observer and multi-observation co∼event [1, 2, 3] is considered less a mathematical model than an art form that requires a multitude of skills, especially the ability to measure human interactions and leverage that knowledge to control observer mistakes and weaknesses. At present, the theory of experience and chance has been tested and has proven to be effective in many applications [4, 5, 6, 7, 3, 8, 9, 10]. I also reasonably hope that this theory as a mathematical theory of observers and observations will contribute to a clearer understanding of quantum mechanics. We will never understand to the end what Bohr thought when he said that clarity is dual to truth. This question is more terminological and philosophical than physical or mathematical. However, today his idea of the existence of something that plays the role of truth, but in some other sense, which complements the truth that we are looking for in the probabilistic world, continues to be more than fruitful. The reason for writing this work was not at all Bohr's statement and the desire to comprehend this statement within the framework of my new theory. It all started with the fact that I needed a mathematical tool for measuring one obvious property of a co∼event, which I would call the scatteredness of the co∼event along (experience) and across (chance) the bra-ket-space. For some reason, it seemed to me that an unclarity should be the most appropriate name for this mathematical measurement tool. And only at this moment, I remembered the Bohr principle of complementarity and his statement about the complementarity of truth and clarity. I do not presume to say how much «my» clarity of a co∼events corresponds to what is complementary to the truth, following Bohr. But since in my theory the co∼event is the mathematical model of the couple, experience and chance, then the unclarity of the co∼event is a normalized measure of the scatteredness of the truth of experience and the truth of chance along and across the space of experience and chance. Therefore, to be honest, the motive of this work was the theory desire to describe and to understand in detail one new numerical characteristic of a co∼event, which measures the scatteredness of the co∼event along (bra) and across (ket) the bra-ket-space.
The Rashomon effect occurs when an event is given contradictory interpretations by the individual... more The Rashomon effect occurs when an event is given contradictory interpretations by the individuals involved. The effect is named after Akira Kurosawa's 1950 lm Rashomon, in which a murder is described in four contradictory ways by four witnesses [1]. The term addresses the motives, mechanism, and occurrences of the reporting on the circumstance and addresses contested interpretations of events, the existence of disagreements regarding the evidence of events and subjectivity versus objectivity in human perception, memory, and reporting. Lurking behind the theory of experience and chance, co∼eventum mechanics [2, 3, 4], and our modern understanding of mind and matter is the simple idea of co∼event. And among scientists, there is growing confidence that focusing on a co∼event is becoming more and more productive than it once was. Here we consider the co∼eventum mechanistic approach with the co∼eventum mechanistic Bayesian theorems [5] to analyze the Rashomon case in forensics.
Proc. of the XVII Intern. FAMEMS-2018 Conf. on Financial and Actuarial Mathematics and Eventology of Multivariate Statistics & the III Workshop on Hilbert’s Sixth Problem. Krasnoyarsk, SFU, 115-140, 2018
Definitions of the distribution functions of experienced, random, and experienced-random variable... more Definitions of the distribution functions of experienced, random, and experienced-random variables are given. The familiar apparatus of distribution functions is used here to characterize three types of variables that naturally arise in the co$\sim$event mechanics and among which two types, experienced and experienced-random variables, are completely new concepts. The first type, the experienced variable, is the numerical function of past experience and past causes. The second type, a random variable, is a numerical function of a future case and a future consequence. Finally, the third type, experienced-random variable, is a numerical function that relates the past experience of the observer with the future case of observation, i.e. past cause with future consequence. These definitions are illustrated by a large number of examples that have a transparent interpretation in numerous applications.
I will remind you that the theory of experience and chance is based on the dual axiomatics of co∼events, which includes Kolmogorov's axiomatics of probability theory as one of the dual halves [1, 2, 3]. Defined by this axiomatics the duality of a co∼event leads to the duality of any numerical superstructure of this new theory, which also, as its co∼event foundation, includes the classical concept of a random variable (r.v.) as a dual reflection of the new concept of an experienced variable (e.v.), and introduces a fundamentally new concept of experienced-random variable (e-r.v.) defined on the Cartesian product ⟨Ω|Ω⟩ = ⟨Ω| × |Ω⟩ of the space of elementary experienced (accumulated) incomes ⟨Ω| and the space of elementary random outcomes |Ω⟩.
Proceedings of the XVII Conference on FAMEMS and the III Workshop on Hilbert's sixth problem. Krasnoyarsk, SFU, 44-53, 2018
We live in the real world, at such a time and in such circumstances, when not only principles, bu... more We live in the real world, at such a time and in such circumstances, when not only principles, but also facts blur, become overgrown with lies and pretense. The endless cycle of our indefinite co∼being forces observers to look for tools capable of coping with the challenges of uncertainty world, which would make it possible to comprehend, express and measure vague principles, facts, lies and pretense. However, note that we have always lived, we live and we will live in the world of co∼events which is mathematically controlled by the theory of experience and chance and the co∼eventum mechanics. The main tools of these new theories are two measures: probabilistic and believabilistic, which are intended to comprehend, express and measure our co∼eventum world. The probability measures the future chance of an observation, the believability measures the past experience of an observer. This paper shows that these two measures are naturally related to each other in the co∼eventum mechanistic H-theorem, and this connection between the past uncertainty of experience and the future uncertainty of chance is expressed using the Gibbs distribution, which is based on the extreme entropy conditions.
A co∼eventum mechanistic generalization of the eventological H-theorem is proposed, which determines the extreme-entropy properties of Gibbs distributions in the co∼eventum mechanics where Gibbs distributions relate the past experience of observers with the future chance of observations. The co∼eventum mechanistic H-theorem, a co∼eventum generalization of the Boltzmann 𝐼-theorem from statistical mechanics, justifies the application of Gibbs distributions of co∼events minimizing relative entropy, as statistical models of the behavior of a rational subject, striving for an equilibrium co∼eventum choice between the past experience and the future chance in various spheres of her/his co∼being.
Proceedings of the XVII FAMEMS Conference and III Workshop on Hilbert's sixth problem, Krasnoyarsk, SFU, 9-21, 2018
A significant extension of the eventological H-theorem, first proved in [2008], is proposed. This... more A significant extension of the eventological H-theorem, first proved in [2008], is proposed.
This extended H-theorem is an eventological generalization
for the Boltzmann H-theorem from statistical mechanics and justifies the application of Gibbs and hyperbolic distributions of sets of events that minimize entropy and two relative entropies, for the statistical modeling the behavior of a rational subject, when s/he striving for an equilibrium eventological choice between experience and chance in various spheres of her/his co-existence with the world.
Proceedings of the XVII Conference on FAMEMS and the III Workshop on Hilbert's sixth problem. Krasnoyarsk, SFU, 9-21, 2018
A significant extension of the eventological H-theorem, first proved in 2008, is proposed. This e... more A significant extension of the eventological H-theorem, first proved in 2008, is proposed. This extended H-theorem is an eventological generalization for the Boltzmann H-theorem from statistical mechanics and justifies the application of Gibbs and hyperbolic distributions of sets of events that minimize entropy and two relative entropies, for the statistical modeling the behavior of a rational subject, when s/he striving for an equilibrium eventological choice between experience and chance in various spheres of her/his co-existence with the world.
THE XV CONFERENCE ON FAMEMS AND OPEN SEMINAR ON THE SIXTH GILBERT PROBLEM , KRASNOYARSK , SIBERIA , RUSSIA , 2016
The aim of the paper is the axiomatic justification of the theory of experience and chance, one of... more The aim of the paper is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author’s main idea was the natural inclusion of Kolmogorov’s axiomatics of probability theory in a number of general concepts of the theory of experience and chance. The analogy between the measure of a set and the probability of an event has become clear for a long time. This analogy also allows further evolution: the measure of a set is completely analogous to the believability of an event. In order to postulate the theory of experience and chance on the basis of this analogy, you just need to add to the Kolmogorov probability theory its dualreflection — the believability theory, so that the theory of experience and chance could be postulated as the certainty (believability-probability) theory on the Cartesian product of the probability and believability spaces, and the central concept of the theory is the new notion of co∼event as a measurable binary relation on the Cartesian product of sets of elementary incomes and elementary outcomes. Attempts to build the foundations of the theory of experience and chance from this general point of view are unknown to me, and the whole range of ideas presented here has not yet acquired popularity even in a narrow circle of specialists; in addition, there was still no complete system of the postulates of the theory of experience and chance free from unnecessary complications. Postulating the theory of experience and chance can be carried out in different ways, both in the choice of axioms and in the choice of basic concepts and relations. If one tries to achieve the possible simplicity of both the system of axioms and the theory constructed from it, then it is hardly possible to suggest anything other than axiomatization of concepts co∼event and its certainty (believability-probability). The main result of this work is the axiom of co∼event, intended for the sake of constructing a theory formed by dual theories of believabilities and probabilities, each of which itself is postulated by its own Kolmogorov system of axioms. Of course, other systems of postulating the theory of experience and chance can be imagined, however, in this work, a preference is given to a system of postulates that is able to describe in the most simple manner the results of what I call an experienced-random experiment.
Proceedings of the XI International FAMES'2012 Conference. Oleg Vorobyev, ed. - Krasnoyarsk: SFU, - 423 p., 2012
An eventological model of a mean-probable event for a set of events is proposed, which has analo... more An eventological model of a mean-probable event for a set of events is proposed, which has analogies with the concept of a mean-measure set that we introduced earlier.
(see also in English https://www.academia.edu/2328936/)
II FAM-2003 All-Russian Conference, Krasnoyarsk State University, Krasnoyarsk, 2003
The paper proposes a theory of sets of symmetric events, i.e. sets of events such that the probab... more The paper proposes a theory of sets of symmetric events, i.e. sets of events such that the probabilities of the intersection of equally powerful subsets are equal to each other. The properties of the sets of symmetric events are considered in detail, and a number of statements about their event-probability distributions are proved. The proposed theory of sets of symmetric events has numerous applications not only in probability theory but also in physics and other areas of natural science and the humanities.
Proceedings of the XV FAMEMS-2016 Conference on Financial and Actuarial Math and Eventology of Multivariate Statistics (Oleg Vorobyev ed.), Kranoyarsk, SFU, 2016
The aim of the paper is the axiomatic justification of the theory of experience and chance, one o... more The aim of the paper is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the
Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of probability theory in a number of general concepts of the theory of experience and chance. The analogy between the measure of a set and the probability of an event has become clear for a long time. This analogy also allows further evolution: the measure of a set is completely analogous to the believability of an event. In order to postulate the theory of experience and chance on the basis of this analogy, you just need to add to the Kolmogorov probability
theory its dual reflection --- the believability theory, so that the theory of experience and chance could be postulated as the certainty
(believability-probability) theory on the Cartesian product of the probability and believability spaces, and the central concept of the theory is the new notion of co~event as a measurable binary relation on the Cartesian product of sets of elementary incomes and elementary outcomes. Attempts to build the foundations of the theory of experience and of chance from this general point of view are unknown to me, and the whole range of ideas presented here has not yet acquired popularity even in a narrow circle of specialists; in addition, there was still no complete system of the postulates of the theory of experience and chance free from unnecessary complications. Postulating the theory of experience and chance can be carried out in different ways, both in the choice of axioms and in the choice of basic concepts and relations. If one tries to achieve the possible simplicity of both the system of axioms and the theory constructed from it, then it is hardly possible to suggest anything other than axiomatization of concepts co~event and its certainty (believability-probability). The main result of this work is the \textbf{axiom of co~event}, intended for the sake of constructing a theory formed by dual theories of believabilities and probabilities, each of which itself is postulated by its own Kolmogorov system of axioms. Of course, other systems of postulating the theory of experience and chance can be imagined, however, in this work, a preference is given to a system of postulates that is able to describe in the most simple manner the results of what I call an experienced-random experiment.
Proceedings of the VII FAM Conference, Krasnoyarsk, Siberian Federal University Press, 2008
A thorough introduction to the theory of multicovariance of events is given, the beginnings of wh... more A thorough introduction to the theory of multicovariance of events is given, the beginnings of which are fragmentarily presented in [https://www.academia.edu/38605343, https://www.academia.edu/189393].
A multicovariance is a multiplicative version of the measure of the dependence of events and serves as a convenient tool for analyzing the structures of event dependencies, successfully complementing the traditional additive variant of the measure of the dependence of events, a covariance.
The theory of multicovariances of events is indispensable in the study of the classes of Gibbs and anti-Gibbs eventological distributions that associate probability with the entropy, information and value of events; as well as in the analysis and solution of the variational problems of the eventological information theory, in which they look for the equilibrium eventological distributions of the sets of events, providing an extreme of entropy or relative entropy under various kinds of restrictions on certain subsets of events.
In addition, the eventological multicovariance theory is effectively used in numerous eventology applications for modeling humanitarian and socioeconomic systems.
Proceedings of the XIII FAMEMS-2014 Conference on Financial and Actuarial Math and Eventology of Multivariate Statistics (Oleg Vorobyev ed.), Kranoyarsk, SFU Press, 2014
The author has developed a general theory for measuring the statistical interconnections between ... more The author has developed a general theory for measuring the statistical interconnections between events, called ``mathematical eventology'' \cite[2007]{Vorobyev2007}, \cite[2011]{Vorobyev2011em}. The paper represents fresh ``eventological'' ideas that radically rethinking the basis of previous approaches to measuring statistical interconnections of events beyond the traditional measurements in the probability theory and mathematical statistics, adding to the already well-known methods of measuring association, or statistical dependency, another new group of methods of measuring agreement of a set of events.
It shows by useful ``total'' quantities (called agreement, association, covariance, set-distance, set-nearness, and set-closeness of a set of events) formulas in this context can be simplified and elegantly summarized for many applications, including for the correct generalization of the traditional indicators of statistical interconnections of events as Pearson correlation, Yule association, as well as a popular index of agreement --- Cohen kappa \cite[1960]{Cohen1960}.
Proposed new methods demonstrate the growing potential of ``eventological'' technologies in the study of structures of interconnections (agreement, association, or statistical dependency) of events, which applies to the measurement in the nominal (categorical), and the ordered and numeric (difference, ratio) scales.
The development and use in a variety of applications of the new concept of the set-distance for a set of events must have necessarily come into contact with the area of modern multivariate statistics that deals with measuring the commonality (agreement) of experts in estimates within categorical (nominal) scales. The results of this dramatic contact are set forth below. As the ``whipping boy'', the most popular group of such statistics is chosen: the kappa-indicators of the commonality (agreement) of experts in estimates within categorical scales.
The aim of the paper is the axiomatic justification of the theory of experience and of chance, on... more The aim of the paper is the axiomatic justification of the theory of experience and of chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of probability theory in a number of
general concepts of the theory of experience and of chance. The analogy between the measure of a set and the probability of an event has become clear for a long time. This analogy also allows further evolution: the measure of a set is completely analogous to the believability of an event.
In order to postulate the theory of experience and of chance on the basis of this analogy, you just need to add to the Kolmogorov probability theory its dual reflection --- the believability theory, so that the theory of experience and of chance could be postulated as the certainty
(believability-probability) theory on the Cartesian product of the probability and believability spaces, and the central concept of the theory is the new notion of co$\sim$event as a measurable binary relation on the Cartesian product of sets of elementary incomes and elementary outcomes.
Attempts to build the foundations of the theory of experience and of chance from this general point of view are unknown to me, and the whole range of ideas presented here has not yet acquired popularity even in a narrow circle of specialists; in addition, there was still no complete system of
the postulates of the theory of experience and of chance free from unnecessary complications. Postulating the theory of experience and of chance can be carried out in different ways, both in the choice of axioms, and in the choice of basic concepts and relations. If one tries to achieve the
possible simplicity of both the system of axioms and the theory constructed from it, then it is hardly possible to suggest anything other than axiomatization of concepts co$\sim$event and its certainty (believability-probability). The main result of this work is the \textbf{axiom
co$\sim$event}, intended for the sake of constructing a theory formed by dual theories of believabilities and probabilities, each of which itself is postulated by its own Kolmogorov system of axioms. Of course, other systems of postulating the theory of experience and of chance can be
imagined, however, in this work a preference is given to a system of postulates that is able to describe in the most simple manner the results of what I call an experienced-random experiment.
We introduce the set-theoretic language for the element-set labelling a Cartesian product by meas... more We introduce the set-theoretic language for the element-set labelling a Cartesian product by measurable binary relations intended for the
labelling, or for the naming of parts and details of the construction that we are going to propose in the theory of experience and of chance as a
mathematical model of an event as a dual pair.
This work is the third, but not the last, in the cycle begun by the works \cite{Vorobyev2016famem... more This work is the third, but not the last, in the cycle begun by the works \cite{Vorobyev2016famems1, Vorobyev2016famems2} about the new
theory of experience and chance as the theory of co~events. Here I introduce the concepts of two co~event means, which serve as dual co~event characteristics of some co~event. The very idea of dual co~event means, has become the development of two concepts: mean-measure set \cite{Vorobyev1984} and mean-probable event \cite{Vorobyev2012fames4, Vorobyev2013sfu}, which were first introduced as two independent characteristics of the set of events, so that then, within the framework of the theory of experience and chance, the idea can finally get the opportunity to appear as two dual faces of the same co~event. I must admit that, precisely, this idea, hopelessly long and lonely stood at the sources of an indecently long string of guesses and insights, did not tire of looming, beckoning to the new co~event description of the dual nature of uncertainty, which I called the theory of experience and chance or the certainty theory. The constructive final push to the idea of dual co~event means has become two surprisingly suitable examples, with which I was fortunate to get acquainted in 2015, each of which is based on the statistics of the experienced-random experiment in the form of a co~event.
Eventology, theory of experience and chance, event, co~event, experience, chance, to happen, to experience, to occur, probability,
believability, mean-believable (mean-experienced) terraced bra-event, mean-probable (mean-possible) ket-event, mean-believable-probability
(mean-experienced-possible) co~event, experienced-random experiment, the dual event means, the dual co~event means, bra-means, ket-means, Bayesian analysis, approval voting, forest approval voting.
The eventological H-theorem is proved, which completes the H-theorem Boltzmann of statistical mec... more The eventological H-theorem is proved, which completes the H-theorem Boltzmann of statistical mechanics and serves mathematical justification (mathematically not less than convincing than the H-theory of Boltzmann for the second thermodynamics) of what can be called the "second beginning of eventology" justifying the application of Gibbs and ``anti-Gibbs'' distributions of sets of events minimizing relative entropy, as statistical models of behavior of reasonable subject, striving for an equilibrium eventological choice between perception and activity in various areas of his developments.
An essence of eventological formalism and its components, nominal, terraced, standard, set-phenom... more An essence of eventological formalism and its components, nominal, terraced, standard, set-phenomenon, and Kopula formalism, is presented briefly.
A new in probability theory and eventology notion of Kopula (eventological copula) is introduced.... more A new in probability theory and eventology notion of Kopula (eventological copula) is introduced. The theorem on characterizing a set of events by Kopula serves as eventological prototype for well-known Sklar's theorem on copulas (1959) is proved. Examples of Kopulas of doublets and triplets of events and of also some N-sets of events are given.
Since the 50s of the last century there is the classical theory of copula, which allows you to build classes of joint distribution functions with the given marginal distribution functions.
In eventology, events set theory, proposed the theory of Kopulas (eventological copula) allows us to solve a similar problem, to build e.p.d. classes of sets of events, events of which occur with a given probability of marginal events (marginal probabilities).
An extension of the notion of set-distance of an N-set of events characterizing its disagreement ... more An extension of the notion of set-distance of an N-set of events characterizing its disagreement to (N+1)-family of set-distances of different orders is considered. This family of disagreement indexes called set-distogram of a set of events characterizes the distribution of disagreement of events relative to the power of subsets of the given set of events and serves as a convenient tool for measuring the detailed disagreement of the set of events. Examples of set-distogram for some types of probability distributions of sets of events with different structures of agreement and disagreement.
Some foundations of the eventological method are discussed. New notions of the universal K-event ... more Some foundations of the eventological method are discussed. New notions of the universal K-event (the universal Kolmogorov event) and the c'o-event (the name of universal K-event) are defined. The sixth eventological axiom of c'o-event is formulated from which proposed earlier axioms VI and VII follow. New concepts of a set-product and an ordered set-product of sets of c'o-events are introduced that differ from the usual concepts of direct and Cartesian products significantly.
Mean-phenomenon portfolio problem is formulated. Mean-phenomenon variant direct eventological Mar... more Mean-phenomenon portfolio problem is formulated. Mean-phenomenon variant direct eventological Markowitz problem is considered. This statement study all phenomena at once and the result is the distribution of the portfolios of events, which is effective for all phenomena in mean. In this paper we also consider a mean-phenomenon model of pair funding strategy: Bulls and Bears.
An extension of the notion of set-distance of an NNN-set of events characterizing its disagreemen... more An extension of the notion of set-distance of an NNN-set of events characterizing its disagreement to (N+1)(N+1)(N+1)-family of set-distances of different orders is considered. This family of disagreement indexes called set-distogram of a set of events characterizes the distribution of disagreement of events relative to the power of subsets of the given set of events and serves as a convenient tool for measuring the detailed disagreement of the set of events. Examples of set-distogram for some types of probability distributions of sets of events with different structures of agreement and disagreement.
Proceedings of the XIV FAMEMS-2015 Conference on Financial and Actuarial Math and Eventology of Multivariate Statistics (Oleg Vorobyev ed.), Krasnoyarsk, SFU, 2015
Any set of events has the unique own ordered set of half-rare events (o.s.h-r.e.) that characteri... more Any set of events has the unique own ordered set of half-rare events (o.s.h-r.e.) that characterizes the set of events in the following sense: its event probability distribution (e.p.d.) is connected to the e.p.d. of the o.s.h-r.e. by mutually inverse renumbering and event permutations.
Proceedings of the XII FAMES-2013 Conference on Financial and Actuarial Math and Eventology of Safety. Krasnoyarsk, SFU, 40-49, 2013
Totals of the eventological safety system modeling is considered for examples and illustrations, ... more Totals of the eventological safety system modeling is considered for examples and illustrations, which are intended to demonstrate the main features of the algorithm for calculating the risk of a dangerous event at the company under established the event-related circumstances based on the portfolio of identification indicators of company safety; inter alia the examples and illustrations show the role and functions (in calculating the risk) of the three main event-based figurants in the safety eventological system: the total subject, the total object and the total barrier; and most importantly they reveal the key of eventological approach applicability for the field of safety in the methods for selecting the optimal portfolio of identification indicators of safety providing specified accuracy of estimating risk of the dangerous event for this company by minimal expert costs. 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/
Mean-phenomenon portfolio problem is formulated. Mean-phenomenon variant direct eventological Mar... more Mean-phenomenon portfolio problem is formulated. Mean-phenomenon variant direct eventological Markowitz problem is considered. This statement study all phenomena at once and the result is the distribution of the portfolios of events, which is effective for all phenomena in mean. In this paper we also consider a mean-phenomenon model of pair funding strategy: Bulls and Bears.