scholarly journals Geometric interpretation of subjective probability: random numbers and objective conditions of coherence

2016 ◽  
Vol 4 (2) ◽  
pp. 90
Author(s):  
Pierpaolo Angelini ◽  
Antonio Maturo
Keyword(s):  
Probability Theory ◽  
Coordinate System ◽  
Subjective Probability ◽  
Geometric Interpretation ◽  
Psychological Aspect ◽  
Random Numbers ◽  
Metric Properties ◽  
Probabilistic Evaluation ◽  
The Individual

In the domain of the logic of certainty we study the objective notions of the subjective probability with the clear aim of identifying their fundamental characteristics before the assignment, by the individual, of the probabilistic evaluation: probability is an additional and subjective notion that one applies within the range of possibility, thus giving rise to those gradations, more or less probable, that are meaningless in the logic of certainty. When we study the criteria for evaluations under conditions of uncertainty and their corresponding conditions of coherence we show an inevitable dichotomy between the subjective or psychological aspect of probability and the objective or logical or geometrical one. The affine properties are the basis of essential concepts of probability theory and only they make sense, being independent of the choice of a coordinate system; however, the importance of the metric properties appears in order to represent random numbers and analytical conditions of coherence.

scholarly journals On the Dichotomy between the Psychological or Empirical Aspect of Subjective Probability and the Logical or Geometrical One

2016 ◽  
Vol 5 (4) ◽  
pp. 59
Author(s):  
Pierpaolo Angelini ◽  
Antonio Maturo
Keyword(s):  
Subjective Probability ◽  
Operational Definition ◽  
Probabilistic Evaluation ◽  
Definition Of ◽  
The Individual ◽  
Entire Theory

In the domain of the logic of certainty we examine the objective notions of the subjective probability with the clear aim of identifying their fundamental characteristics before the assignment, by the individual, of the probabilistic evaluation. Probability is an additional and subjective notion that one applies within the range of possibility, thus giving rise to those gradations, more or less probable, that are meaningless in the logic of certainty. Each criterion for evaluations under conditions of uncertainty is a device or instrument for obtaining a measurement; it furnishes an operational definition of probability or prevision P and together with the corresponding conditions of coherence can be taken as a foundation for the entire theory of probability. When we examine these criteria and their corresponding conditions of coherence we show the inevitable dichotomy between the subjective or psychological or empirical aspect of probability and the objective or logical or geometrical one.

Probability Theory for Fuzzy Quantum Spaces with Statistical Applications

2017 ◽  
Author(s):  
Renáta Bartková ◽  
Beloslav Riečan ◽  
Anna Tirpáková
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Ergodic Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematics Students ◽  
Intuitionistic Fuzzy ◽  
Individual Ergodic Theorem ◽  
Recurrence Theorem ◽  
The Individual ◽  
Atanassov Intuitionistic Fuzzy Sets

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem). This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.

DIGITAL TRANSFORMATION OF SOCIO-ECONOMIC RELATIONS AND THE PROBLEM OF THEIR LEGAL REGULATIONS

2021 ◽  
Author(s):  
Ольга Юрьевна Колесникова
Keyword(s):  
Artificial Intelligence ◽  
Coordinate System ◽  
Legal Regulation ◽  
Digital Transformation ◽  
Legal Regulations ◽  
Work Analysis ◽  
Economic Relations ◽  
The Individual

Актуальность работы обусловлена цифровой трансформацией социально-экономических отношений и необходимостью исследований их правового регулирования в системе координат “индивидуум - общество - цифровизация - роботы - искусственный интеллект”. Цель работы: анализ тенденций цифровизации социально-экономических отношений и предопределяемой этими отношениями проблемы их правового регулирования. The relevance of the work is due to the digital transformation of socio-economic relations and the need to research their legal regulation in the “individual - society - digitalization - robots - artificial intelligence” coordinate system. Purpose of the work: analysis of trends in the digitalization of socio-economic relations and the problem of their legal regulation predetermined by these relations.

De-biasing role induced bias using Bayesian networks

2019 ◽  
Author(s):  
Mark Schweizer
Keyword(s):  
Probability Theory ◽  
Bayesian Networks ◽  
Subjective Probability ◽  
Ad Hoc ◽  
Decision Aids ◽  
Decision Makers ◽  
Normative Standard ◽  
The Many ◽  
Legal Fact ◽  
Assessment Of Evidence

Abstract The merits of using subjective probability theory as a normative standard for evidence evaluation by legal fact-finders have been hotly debated for decades. Critics argue that formal mathematical models only lead to an apparent precision that obfuscates the ad-hoc nature of the many assumptions that underlie the model. Proponents of using subjective probability theory as normative standard for legal decision makers, specifically proponents of using Bayesian networks as decision aids in complex evaluations of evidence, must show that formal models have tangible benefits over the more natural, holistic assessment of evidence by explanatory coherence. This article demonstrates that the assessment of evidence using a Bayesian network parametrized with values obtained from the decision makers reduces role-induced bias, a bias that has been largely resistant to de-biasing attempts so far.

scholarly journals Statistical characteristics of sources of vehicle kinematic excitation

2020 ◽  
Vol 313 ◽  
pp. 00011
Author(s):  
Jozef Melcer ◽  
Eva Merčiaková ◽  
Mária Kúdelčíková
Keyword(s):  
Probability Theory ◽  
Spectral Density ◽  
Surface Quality ◽  
Correlation Functions ◽  
Random Variable ◽  
Point Of View ◽  
Statistical Characteristics ◽  
Kinematic Excitation ◽  
Power Spectral ◽  
The Individual

The longitudinal and transverse road profiles represent the functions of a random variable from a mathematical point of view. It is appropriate to use methods of probability theory and mathematical statistics for their description. The unevenness of the runway surface is the main source of the vehicle's kinematic excitation. This paper describes the statistical properties of the mapped road profiles. It shows a way of categorizing road surface quality based on the power spectral density of unevenness. The interrelationships between the individual points of the profile and the profiles with one another are evaluated by correlation functions.

A Component-Centric Approach to Structural Analysis of Mechanisms

2014 ◽  
Author(s):  
Christopher Stack ◽  
Subha Kumpaty ◽  
Mohammad Mahinfalah
Keyword(s):  
Structural Analysis ◽  
Coordinate System ◽  
The Other ◽  
Component Level ◽  
Unique Problem ◽  
Separate Model ◽  
Loading Effects ◽  
Level Model ◽  
Good Trade ◽  
The Individual

Structural analyses of mechanisms with components that move relative to each other provide a unique problem to the analyst building and running structural models. In these situations, the analyst usually has to either simplify the problem to a point where the results are unusable or maintain multiple models, which will take more effort to maintain and more resources to run the models. If a mechanism is simplified down to just analyzing one component at a time without regard for the other components in the system, the results will not be accurate because the loading effects of the other components will not be accounted for. In cases where all the components are included in the model the loading effects from the other components will be accounted for, however, a separate model will be required for each position. This paper presents a method of breaking down the complex mechanism into a component level model for each part of the assembly, while still accounting for all loading effects of the other components; in the Pivot Method the component under analysis stays stationary and the loading moves around the component to represent the different positions that it can take. In order to accomplish this task, a simplified model is used to generate loads at each of the joints. Once the pivot loads are known, a spreadsheet can be used to transform the loads to a coordinate system in which the individual component is being modeled. With the pivot loads known and all the loads transformed into the proper coordinate system the structural analysis of the component under investigation can continue. The intention of this paper is to introduce the Pivot Method and to demonstrate that it provides a good trade off between both the complexity of methods that model the assembly as a system, and those that focus on the component under question alone. To accomplish this, the analysis results of the Pivot Method models will be compared to results obtained from other methods, with the intention of showing that the Pivot Method will provide the same results while requiring less effort to model and less resources to run.

scholarly journals SYSTEM FOR MEASURING KINEMATICS OF VESTIBULAR SYSTEM MOVEMENTS IN NEUROLOGICAL PRACTICE

2016 ◽  
Vol 56 (4) ◽  
pp. 336-343 ◽  
Author(s):  
Petr Volf ◽  
Patrik Kutílek ◽  
Jiří Hozman ◽  
Rudolf Černý ◽  
Tomáš Koukolík ◽  
...  
Keyword(s):  
Coordinate System ◽  
Vestibular System ◽  
Head Impulse Test ◽  
Clinical Neurology ◽  
Head Impulse ◽  
Left And Right ◽  
The Individual ◽  
Medical Examinations

The article deals with the design of a system for studying kinematics of movement of the vestibular system. Up to now there has not existed a system which would enable to measure the kinematic quantities of movement of the individual parts of the vestibular system within its coordinate system. The proposed system removes these deficiencies by suitable positioning of five gyro-accelerometric units on the helmet. The testing of the system took place under two conditions, during Unilateral Rotation on Barany Chair and Head Impulse Test. During the testing, the system justified its application because the results show that the kinematic quantities of the movement of the left and right labyrinths of the vestibular system differ. The introduced device is mainly intended for application in clinical neurology with the aim to enable the physician to measure all linear and angular accelerations of the vestibular system during medical examinations.

Bayesian Statistics and Political Recruitment: A Comment

1976 ◽  
Vol 6 (1) ◽  
pp. 124-125
Author(s):  
Paul Whiteley
Keyword(s):  
Bayesian Statistics ◽  
Bayesian Approach ◽  
Subjective Probability ◽  
Analytical Techniques ◽  
Political Activism ◽  
Background Characteristics ◽  
Political Recruitment ◽  
Political Activist ◽  
The Individual ◽  
The Bayesian Approach

In an important contribution to the improvement of data analytical techniques in political science, Budge and Farlie examine the predictive success of various background characteristics in determining political activism [Ian Budge and Dennis Farlie, ‘Political Recruitment and Dropout’, this Journal, v (1975), 33–68]. The authors use the framework of Bayesian statistics, in which the subjective probability that a given individual will be a political activist is revised in the light of sample information about the background characteristics of activists to give a posterior (i.e. after the information or event) probability that the individual is an activist. Unfortunately, as the authors admit, they do not utilize fully all the components of the Bayesian approach.

scholarly journals Quantum Bayesianism as the basis of general theory of decision-making

2016 ◽  
Vol 374 (2068) ◽  
pp. 20150245 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Decision Making ◽  
Probability Theory ◽  
Subjective Probability ◽  
Quantum Probability ◽  
Total Probability ◽  
Interpretation Of Quantum Mechanics ◽  
Classical Probability ◽  
Probability Interpretation ◽  
Formula Of Total Probability

We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability—one the basic laws of classical probability theory.

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