A result in renyi's conditional probability theory with application to subjective probability

1983 ◽  
Vol 12 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Roger M. Cooke
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Subjective Probability

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.

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 Disintegration and Bayesian inversion via string diagrams

2019 ◽  
Vol 29 (7) ◽  
pp. 938-971 ◽  
Author(s):  
Kenta Cho ◽  
Bart Jacobs
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Opposite Direction ◽  
Bayesian Inversion ◽  
Conditional Probabilities ◽  
Discrete Probability ◽  
Joint State

AbstractThe notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability – via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

scholarly journals 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.

Some New Aspects of Slamming Probability Theory

1978 ◽  
Vol 22 (03) ◽  
pp. 186-192
Author(s):  
Harilaos N. Psaraftis
Keyword(s):  
Probability Theory ◽  
Poisson Process ◽  
Conditional Probability ◽  
Systematic Investigation ◽  
Unconditional Probability ◽  
Deck Wetness

A systematic investigation of some probabilistic aspects of slamming is presented. This investigation includes the assessment of the unconditional probability of slamming at a random instant of time; the estimation of the conditional probability of slamming at a given instant after a particular slam; and the consequent rejection of the hypothesis that slamming is a Poisson process. In addition, a procedure to approximate the distribution of slamming interarrival times2 is presented. Finally, new slamming statistics, obtainable from the theory of this work, are presented and compared with the existing slamming criteria. The theory of this paper can be readily applied to other seakeeping events such as deck wetness, keel emergence, and propeller racing.

Sign in / Sign up

Export Citation Format

Share Document