For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've nally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼ventum mechanics in the most.

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The main objective of co∼eventum mechanics 1 and eventology 2 is the penetration of a new event-based language into all scientic 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 unies, in the rst place, socio-humanitarian, ecological, psycho-economic and other spheres, where scientic and technological research is dicult 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. 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.

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∼eventum mechanics in the. moreFor 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∼eventum mechanics in the most approachable way.

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. The overwhelming majority of quantitative work in sociology reports levels of statistical significance.

Often, significance is reported with little or no discussion of what it actually entails philosophically, and this can be problematic Get probability homework help from expert online tutors at, available 24/7. Advanced Probability Theory Stats Homework, assignment and Project Help, Advanced ocr critical thinking f501 mark scheme case study planter type paper on..

moreThe overwhelming majority of quantitative work in sociology reports levels of statistical significance. Often, significance is reported with little or no discussion of what it actually entails philosophically, and this can be problematic when analyses are interpreted.

Often, significance is understood to represent the probability of the null hypothesis (usually understood as a lack of relationship between two or more variables). The first section of this paper deals with this common misunderstanding. The second section gives a history of significance testing in the social sciences, with reference to the historical foundations of many common misinterpretations of significance testing.

The third section is devoted to a discussion of the consequences of misinterpreting statistical significance for sociology. It is argued that reporting statistical significance provides sociology with very little value, and that the consequences of misinterpreting significance values outweighs the benefits of their use.

1 Prior probabilities and the inverse probability error: why P(D|H) = P(H| D) Although quantitative sociology has been challenged on ontological and epistemological grounds, it is still the dominant form of research in many of the largest and most prestigious sociological journals currently in print. However, the statistical tradition that sociology has inherited form psychology and the biological sciences is not an aspect of sociological history readily available for students or researchers.

Indeed, many statistical procedures are ill-understood by the quantitative sociologists who use them. In particular, procedures that measure levels of so-called " statistical significance " are rarely used with the inherent philosophical limitations of those procedures in mind. This is due, in part, to the hybridization of two theories of statistical significance that have disparate theoretical conceptions by statisticalBookmarkIn this paper we propose a generalised maximum-entropy classification framework, in which the empirical expectation of the feature functions is bounded by the lower and upper expectations associated with the lower and upper probabilities.

moreIn this paper we propose a generalised maximum-entropy classification framework, in which the empirical expectation of the feature functions is bounded by the lower and upper expectations associated with the lower and upper probabilities associated with a belief measure. This generalised setting permits a more cautious appreciation of the information content of a training set.

We analytically derive the Karush-Kuhn-Tucker conditions for the generalised max-entropy classifier in the case in which a Shannon-like entropy is adopted. BookmarkIn this paper we build on previous work on the geometry of Dempster's rule to investigate the geometric behaviour of various other combination rules, including Yager's, Dubois', and disjunctive combination , starting from the case of.

moreIn this paper we build on previous work on the geometry of Dempster's rule to investigate the geometric behaviour of various other combination rules, including Yager's, Dubois', and disjunctive combination , starting from the case of binary frames of discernment. Believabil-ity measures for unnormalised belief functions are also considered.

A research programme to complete this analysis is outlined. Keywords: Geometry · Yager's and Dubois' combination · conjunctive and disjunctive combination · unnormalised belief functions.

BookmarkThe notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This gen-eralises the traditional likelihood function, and.

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This gen-eralises the traditional likelihood function, and provides a natural setting for belief inference from statistical data.

Factorisation results are proven for the case in which conjunctive or disjunctive combination are employed, leading to analytical expressions for the lower and upper likelihoods of 'sharp' samples in the case of Bernoulli trials, and to the formulation of a generalised logistic regression framework View Probability Theory Research Papers on Academia.edu for free. Average case complexity, in order to be a useful and reliable measure, has to be robust..

BookmarkRandom set theory, originally born within the remit of mathematical statistics, lies nowadays at the interface of statistics and AI. Arguably more mathematically complex than standard probability, the field is now facing open issues such.

moreRandom set theory, originally born within the remit of mathematical statistics, lies nowadays at the interface of statistics and AI. Arguably more mathematically complex than standard probability, the field is now facing open issues such as the formulation of generalised laws of probability, the generalisation of the notion of random variable to random set spaces, the extension of the notion of random process, and so on.

Frequentist inference with random sets can be envisaged to better describe common situations such as lack of data and set-valued observations. To this aim, parameterised families of random sets (and Gaussian random sets in particular) are a crucial area of investigation.

In particular, we will present some recent work on the generalisation of the notion of likelihood, as the basis for a generalised logistic regression framework capable to better estimate rare events; a random set-version of maximum-entropy classifiers; and a recent generalisation of the law of total probability to belief functions. In a longer-term perspective, random set theory can be instrumental to new robust foundations for statistical machine learning allowing the formulation of models and algorithms able to deal with mission-critical applications ‘in the wild’, in a mutual beneficial exchange between statistics and artificial intelligence.

BookmarkThe theory of belief functions, sometimes referred to as evidence theory or Dempster-Shafer theory, was first introduced by Arthur P Probability theory and mathematical statistics are difficult subjects both for students to designed by Wolfram Research, and MAPLE, a system for doing mathemat- Sequences of Random Variables and Order Statistics . . 351. 13.1..

Dempster in the context of statistical inference, to be later developed by Glenn Shafer as a general. moreThe theory of belief functions, sometimes referred to as evidence theory or Dempster-Shafer theory, was first introduced by Arthur P.

Dempster in the context of statistical inference, to be later developed by Glenn Shafer as a general framework for modelling epistemic uncertainty. Belief theory and the closely related random set theory form natural frameworks for modelling situations in which data are missing or scarce: think of extremely rare events such as volcanic eruptions or power plant meltdowns, problems subject to huge uncertainties due to the number and complexity of the factors involved (e.

climate change), but also the all-important issue with generalisation from small training sets in machine learning.

This tutorial is designed to introduce the principles and rationale of random sets and belief function theory to mainstream statisticians, mathematicians and working scientists, survey the key elements of the methodology and the most recent developments, make practitioners aware of the set of tools that have been developed for reasoning in the belief function framework on real-world problems. Attendees will acquire first-hand knowledge of how to apply these tools to significant problems in major application fields such as computer vision, climate change, and others.

A research programme for the future of random set theory and high impact applications is eventually outlined. BookmarkFor 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∼eventum mechanics in the.

moreFor 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∼eventum mechanics in the most approachable way.

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, for the theory of experience and chance which I axiomatized in 2016 1, 2 .

In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations 4 .

Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ".

Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance.

Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation.

I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics. These slides begin with allusions to the #MeToo phenomenon, specifically an article citing statistics showing that "workplace sexual harassment is highly prevalent," and asks a whole raft of questions abut what lies behind those.

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They continue with a distinction between equating mathematical probabilities and degrees of proof, which Haack rejects, and the role of statistical evidence in court, which of course she accepts.

Such evidence, however, poses a threat of "delusive exactness"; as she shows first with respect to DNA random-match probabilities, and then with respect to epidemiological risk statistics For use in a standard one-term course, in which both discrete and tory where chance experiments can be simulated and the students can get a feeling famous text An Introduction to Probability Theory and Its Applications (New York: We also thank Jessica for her work on the solution manual for the exercises, building..

BookmarkArbitrary nonlinear functions of random variables can always be described as a series of natural powers of the corresponding random variables. Furthermore, random variables can always be expressed in terms of standard random variables.

moreArbitrary nonlinear functions of random variables can always be described as a series of natural powers of the corresponding random variables.

Furthermore, random variables can always be expressed in terms of standard random variables. Thus, nonlinear functions of random variables ultimately can be represented by series of natural power functions of standard random variables.

In this report, the properties of natural power functions for different representative standard random variables are summarized, and their use is exemplified with different practical examples. The standard random variables considered include standard normal, standard uniform, standard exponential, standard Maxwell-Boltzmann, and standard polynomial distributions.

The lognormal distribution is considered as a particular case of study Mathematics Probability Theory and Stochastic Processes questions of probability theory and random processes in 22 chapters, presented in a logical order .

BookmarkI am still on the first stretch of this nomadic exploration, but I think I can begin to answer the question that is guiding this exploration—'how can the Natural-Indigenous Worldview support our understandings of the potential for an. moreI am still on the first stretch of this nomadic exploration, but I think I can begin to answer the question that is guiding this exploration—'how can the Natural-Indigenous Worldview support our understandings of the potential for an anarchist society (i.

for social order without hierarchical domination)?' The key of Natural-Indigenous Worldview that opens the lock of an anarchist society, of a society without hierarchical domination, comes in the Natural-Indigenous Worldview's spiritual ecology.

When we develop the four R's (responsibility, reciprocity, respect, relationships Young 2015 ) through relating to the world in a manner that is facilitated by the spiritual ecology that rises from the Natural-Indigenous Worldview and thus ascribes spirit to all things without regard for the Colonial Modernist Worldview's distinction between 'animate' and 'inanimate', we come to see the world as a single, living, conscious being. The illusion of a discrete distinction between self and other breaks down and we come to see the self (and other selves) as strands in the unified, conscious web of creation.

We come to care for all of creation as we would care for our children, for our partners, for our parents and for our self. Transcending the illusion of discrete individuality we develop a lovingly reciprocal, responsible, respectful and relational orientation to the world that begets virtuous thought, feeling, behavior and being without recourse to hierarchical authority (to punishment and fear of punishment).

Engaging with the world through the spiritual ecology that rises from the Natural-Indigenous Worldview allows the sprouts of human nature to grow to fruition without recourse to hierarchical domination (i. without recourse to attempts to 'help sprouts grow' by pulling on them and the death of the sprouts of human nature portended by such hierarchical folly Meng Zi 2016, 2A2 ).