Probability interpretations

philosophy of probabilityinterpretation of probabilityinterpretations of probabilityfoundations of probabilityinterpretationinterpretation of the concept of probabilityinterpretations of probability theoryinterpreting what is meant by "probabilitynature of the probabilitiesof probability
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance.wikipedia
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Bayesian probability

Bayesiansubjective probabilityBayesianism
Evidential probability, also called Bayesian probability, can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence.
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

Propensity probability

propensitypropensitiesobjective probability
The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises ) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer).
The propensity theory of probability is one interpretation of the concept of probability.

Frequentist probability

frequentistFrequency probabilitystatistical probability
The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises ) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer). Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms.
Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in many trials.

Probability theory

theory of probabilityprobabilityprobability theorist
In answering such questions, mathematicians interpret the probability values of probability theory.
Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.

Sunrise problem

The "sunrise problem" provides an example.
According to the Bayesian interpretation of probability, probability theory can be used to evaluate the plausibility of the statement, "The sun will rise tomorrow."

Philosophy of mathematics

mathematical realismmathematical Platonismmathematics
In axiomatic form, mathematical statements about probability theory carry the same sort of epistemological confidence within the philosophy of mathematics as are shared by other mathematical statements.

Paul Humphreys (philosopher)

Paul Humphreys
Paul Humphreys is a significant contributor to the philosophy of emergent properties, as well as other areas in the Philosophy of science and Philosophy of probability.

Randomness

randomchancerandomly
The events are assumed to be governed by some random physical phenomena, which are either phenomena that are predictable, in principle, with sufficient information (see determinism); or phenomena which are essentially unpredictable.

A Treatise on Probability

Keynes's theory of probabilityTreatise on Probability
Logical probabilities are conceived (for example in Keynes' Treatise on Probability ) to be objective, logical relations between propositions (or sentences), and hence not to depend in any way upon belief.
Keynes's Treatise is the classic account of the logical interpretation of probability (or probabilistic logic), a view of probability that has been continued by such later works as Carnap's Logical Foundations of Probability and E.T. Jaynes Probability Theory: The Logic of Science.

Probability

probabilisticprobabilitieschance
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance.

Game of chance

games of chancechancegaming
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. It has its origins in correspondence discussing the mathematics of games of chance between Blaise Pascal and Pierre de Fermat in the seventeenth century, and was formalized and rendered axiomatic as a distinct branch of mathematics by Andrey Kolmogorov in the twentieth century.

Frank P. Ramsey

Frank RamseyRamseyFrank Plumpton Ramsey
The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage ), the epistemic or inductive interpretation (Ramsey, Cox ) and the logical interpretation (Keynes and Carnap ).

Richard Threlkeld Cox

CoxCox, Richard ThrelkeldRichard Cox
The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage ), the epistemic or inductive interpretation (Ramsey, Cox ) and the logical interpretation (Keynes and Carnap ).

John Maynard Keynes

KeynesMaynard KeynesJ. M. Keynes
Logical probabilities are conceived (for example in Keynes' Treatise on Probability ) to be objective, logical relations between propositions (or sentences), and hence not to depend in any way upon belief. The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage ), the epistemic or inductive interpretation (Ramsey, Cox ) and the logical interpretation (Keynes and Carnap ).

Rudolf Carnap

CarnapRudolph CarnapCarnap, Rudolf
The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage ), the epistemic or inductive interpretation (Ramsey, Cox ) and the logical interpretation (Keynes and Carnap ).

Donald A. Gillies

GilliesGillies, Donald A.D. Gillies
There are also evidential interpretations of probability covering groups, which are often labelled as 'intersubjective' (proposed by Gillies and Rowbottom ).

Statistical inference

inferential statisticsinferenceinferences
Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing.

Estimation theory

parameter estimationestimationestimated
Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing.

Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing.

Ronald Fisher

R.A. FisherR. A. FisherFisher
The physical interpretation, for example, is taken by followers of "frequentist" statistical methods, such as Ronald Fisher, Jerzy Neyman and Egon Pearson.

Jerzy Neyman

NeymanJerzy Spława-NeymanNeyman, Jerzy
The physical interpretation, for example, is taken by followers of "frequentist" statistical methods, such as Ronald Fisher, Jerzy Neyman and Egon Pearson.

Egon Pearson

PearsonEgon Sharpe PearsonPearson, Egon
The physical interpretation, for example, is taken by followers of "frequentist" statistical methods, such as Ronald Fisher, Jerzy Neyman and Egon Pearson.

Mathematics

mathematicalmathmathematician
The philosophy of probability presents problems chiefly in matters of epistemology and the uneasy interface between mathematical concepts and ordinary language as it is used by non-mathematicians.

Blaise Pascal

PascalPascal, BlaisePascalian
It has its origins in correspondence discussing the mathematics of games of chance between Blaise Pascal and Pierre de Fermat in the seventeenth century, and was formalized and rendered axiomatic as a distinct branch of mathematics by Andrey Kolmogorov in the twentieth century.