# 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.