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- Probability_interpretations abstract "The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory.There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities. 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. In such systems, a given type of event (such as the dice yielding a six) tends to occur at a persistent rate, or "relative frequency", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. Thus talking about physical probability makes sense only when dealing with well defined random experiments. 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).Evidential probability, also called Bayesian probability (or subjectivist 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. On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. 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).Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing. The physical interpretation, for example, is taken by followers of "frequentist" statistical methods, such as R. A. Fisher, Jerzy Neyman and Egon Pearson. Statisticians of the opposing Bayesian school typically accept the existence and importance of physical probabilities, but also consider the calculation of evidential probabilities to be both valid and necessary in statistics. This article, however, focuses on the interpretations of probability rather than theories of statistical inference.The terminology of this topic is rather confusing, in part because probabilities are studied within a variety of academic fields. The word "frequentist" is especially tricky. To philosophers it refers to a particular theory of physical probability, one that has more or less been abandoned. To scientists, on the other hand, "frequentist probability" is just another name for physical (or objective) probability. Those who promote Bayesian inference view "frequentist statistics" as an approach to statistical inference that recognises only physical probabilities. Also the word "objective", as applied to probability, sometimes means exactly what "physical" means here, but is also used of evidential probabilities that are fixed by rational constraints, such as logical and epistemic probabilities.It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.".
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- Probability_interpretations wikiPageWikiLink A_Treatise_on_Probability.
- Probability_interpretations wikiPageWikiLink Aleatoricism.
- Probability_interpretations wikiPageWikiLink Aleatory.
- Probability_interpretations wikiPageWikiLink Andrey_Kolmogorov.
- Probability_interpretations wikiPageWikiLink Atom.
- Probability_interpretations wikiPageWikiLink Axiom.
- Probability_interpretations wikiPageWikiLink Bayesian_probability.
- Probability_interpretations wikiPageWikiLink Belief.
- Probability_interpretations wikiPageWikiLink Blaise_Pascal.
- Probability_interpretations wikiPageWikiLink Bruno_de_Finetti.
- Probability_interpretations wikiPageWikiLink Category:Epistemology.
- Probability_interpretations wikiPageWikiLink Category:Interpretation_(philosophy).
- Probability_interpretations wikiPageWikiLink Category:Probability_interpretations.
- Probability_interpretations wikiPageWikiLink Category:Probability_theory.
- Probability_interpretations wikiPageWikiLink Celestial_mechanics.
- Probability_interpretations wikiPageWikiLink Charles_Sanders_Peirce.
- Probability_interpretations wikiPageWikiLink Coherence_(physics).
- Probability_interpretations wikiPageWikiLink Coin.
- Probability_interpretations wikiPageWikiLink Credence_(statistics).
- Probability_interpretations wikiPageWikiLink David_Miller_(philosopher).
- Probability_interpretations wikiPageWikiLink Determinism.
- Probability_interpretations wikiPageWikiLink Dice.
- Probability_interpretations wikiPageWikiLink Donald_A._Gillies.
- Probability_interpretations wikiPageWikiLink Egon_Pearson.
- Probability_interpretations wikiPageWikiLink Electric_charge.
- Probability_interpretations wikiPageWikiLink Electrical_charge.
- Probability_interpretations wikiPageWikiLink Empirical_evidence.
- Probability_interpretations wikiPageWikiLink Entailment.
- Probability_interpretations wikiPageWikiLink Epistemology.
- Probability_interpretations wikiPageWikiLink Estimation_theory.
- Probability_interpretations wikiPageWikiLink Evidence-based_medicine.
- Probability_interpretations wikiPageWikiLink Evidence_based_medicine.
- Probability_interpretations wikiPageWikiLink Exchangeability.
- Probability_interpretations wikiPageWikiLink Exchangeable_random_variables.
- Probability_interpretations wikiPageWikiLink Frank_P._Ramsey.
- Probability_interpretations wikiPageWikiLink Frequency_(statistics).
- Probability_interpretations wikiPageWikiLink Frequency_probability.
- Probability_interpretations wikiPageWikiLink Frequentist_probability.
- Probability_interpretations wikiPageWikiLink Game_of_chance.
- Probability_interpretations wikiPageWikiLink Games_of_chance.
- Probability_interpretations wikiPageWikiLink Infinity.
- Probability_interpretations wikiPageWikiLink Jerzy_Neyman.
- Probability_interpretations wikiPageWikiLink John_Maynard_Keynes.
- Probability_interpretations wikiPageWikiLink Karl_Popper.
- Probability_interpretations wikiPageWikiLink Law_of_large_numbers.
- Probability_interpretations wikiPageWikiLink Laws_of_probability.
- Probability_interpretations wikiPageWikiLink Logic.
- Probability_interpretations wikiPageWikiLink Logical_consequence.
- Probability_interpretations wikiPageWikiLink Ludlow,_Massachusetts.
- Probability_interpretations wikiPageWikiLink Mathematics.
- Probability_interpretations wikiPageWikiLink Negative_probability.
- Probability_interpretations wikiPageWikiLink Patrick_Suppes.
- Probability_interpretations wikiPageWikiLink Paul_Humphreys_(philosopher).
- Probability_interpretations wikiPageWikiLink Philosophy_of_mathematics.
- Probability_interpretations wikiPageWikiLink Philosophy_of_statistics.
- Probability_interpretations wikiPageWikiLink Pierre-Simon_Laplace.
- Probability_interpretations wikiPageWikiLink Pierre_de_Fermat.
- Probability_interpretations wikiPageWikiLink Pignistic_probability.
- Probability_interpretations wikiPageWikiLink Playing_card.
- Probability_interpretations wikiPageWikiLink Principle_of_indifference.
- Probability_interpretations wikiPageWikiLink Prior_probability.
- Probability_interpretations wikiPageWikiLink Probabilistically_checkable_proof.
- Probability_interpretations wikiPageWikiLink Probability.
- Probability_interpretations wikiPageWikiLink Probability_amplitude.
- Probability_interpretations wikiPageWikiLink Probability_axioms.
- Probability_interpretations wikiPageWikiLink Probability_theory.
- Probability_interpretations wikiPageWikiLink Propensity_probability.
- Probability_interpretations wikiPageWikiLink Quantum_mechanics.
- Probability_interpretations wikiPageWikiLink Quantum_physics.
- Probability_interpretations wikiPageWikiLink Radioactive_decay.
- Probability_interpretations wikiPageWikiLink Randomness.
- Probability_interpretations wikiPageWikiLink Reference_class_problem.
- Probability_interpretations wikiPageWikiLink Richard_Threlkeld_Cox.
- Probability_interpretations wikiPageWikiLink Roger_Ludlow.
- Probability_interpretations wikiPageWikiLink Ronald_Fisher.
- Probability_interpretations wikiPageWikiLink Roulette.
- Probability_interpretations wikiPageWikiLink Rudolf_Carnap.
- Probability_interpretations wikiPageWikiLink Seymour_Geisser.
- Probability_interpretations wikiPageWikiLink Six_Sigma.
- Probability_interpretations wikiPageWikiLink Six_sigma.
- Probability_interpretations wikiPageWikiLink Statistical_hypothesis_testing.
- Probability_interpretations wikiPageWikiLink Statistical_inference.
- Probability_interpretations wikiPageWikiLink String_theory_landscape.
- Probability_interpretations wikiPageWikiLink Sunrise_problem.
- Probability_interpretations wikiPageWikiLink Theory_of_justification.
- Probability_interpretations wikiPageWikiLink Thomas_Bayes.
- Probability_interpretations wikiPageWikiLink Thought_experiment.
- Probability_interpretations wikiPageWikiLink Urn_model.
- Probability_interpretations wikiPageWikiLink Urn_problem.
- Probability_interpretations wikiPageWikiLink File:Dice.jpg.
- Probability_interpretations wikiPageWikiLink File:Roulette_wheel.jpg.
- Probability_interpretations wikiPageWikiLink File:Tokyo_Racecourse_3.jpg.
- Probability_interpretations wikiPageWikiLinkText "Probability interpretations".
- Probability_interpretations wikiPageWikiLinkText "interpretation of probability".