User:INic/Frequency probability

John Venn

The problems and paradoxes of the classical interpretation of probability motivated the development of the relative frequency concept of probability.

Most of the mathematics commonly used to make statistical estimates or tests are developed by statisticians who use this concept exclusively. They are usually called frequentists, and their position is called frequentism. A statistician who uses traditional methods of inference is therefore referred to as a frequentist statistician. Frequentism is, by far, the most commonly held view among working statisticians, probability theorists and physicists.

Frequentists talk about probabilities only when dealing with well-defined random experiments. The set of all possible outcomes of a random experiment is called the sample space of the experiment. An event is defined as a particular subset of the sample space that you want to consider. For any event only two things can happen; it occurs or it occurs not. The relative frequency of occurrence of an event, when repeating the experiment, is a measure of the probability of that event.

This is a highly technical and scientific definition of "probability" and doesn't claim to capture all connotations of the concept 'probable' in colloquial speech of natural languages. Compare how the concept of force is used by physicists in a precise manner despite the fact that force is also a concept in many natural languages, used in religious texts for example. However, this seldom causes problem or confusion, as the context usually reveal if it's the scientific concept that is intended or not.

This school is often associated with the names of Jerzy Neyman and Egon Pearson who described the logic of statistical hypothesis testing. Other influential figures of the frequentist school include John Venn, R.A. Fisher, and Richard von Mises.

Alternative views

Bayesianism

The main alternative view, Bayesianism is more popular among decision theorists. Frequentists can't assign probabilities to things ouside the scope of their definition. In particular, frequentists attribute probabilities only to events while Bayesians apply probabilities to arbitrary statements. For example, if one were to attribute a probability of 1/2 to the proposition that "there was life on Mars a billion years ago" one would violate frequentist canons, because neither an experiment nor a sample space is defined here. However, such degree-of-belief assignments of probability to statements are the basis of Bayesian probability theory.

See also

• probability interpretations
• Bayesian probability
• eclectic probability
• probability
• statistics
• statistical regularity
• probability axioms
• games of chance

External links

• Charles Friedman, The Frequency Interpretation in Probability PS
• John Venn, The Logic of Chance

Bibliography

• P W Bridgman, The Logic of Modern Physics, 1927
• Alonzo Church, The Concept of a Random Sequence, 1940
• Harald Cramér, Mathematical Methods of Statistics, 1946
• P Martin-Löf, On the Concept of a Random Sequence, 1966
• Richard von Mises, Probability, Statistics, and Truth, 1939 (German original 1928)
• Jerzy Neyman, First Course in Probability and Statistics, 1950
• Hans Reichenbach, The Theory of Probability, 1949 (German original 1935)
• Bertrand Russell, Human Knowledge, 1948
• John Venn, The Logic of Chance, 1866