# Frequency probability

Statistical regularity has motivated the development of the relative frequency concept of probability.

Most of the procedures commonly used to make statistical estimates or tests were developed by statisticians who used this concept exclusively. They are usually called frequentists, and their position is called frequentism. A statistician who uses traditional methods of inference is therefore possibly referred to as a frequentist statistician. Put another way: a frequentist statistician is a statistician who does not practise Bayesian statistics.

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.

Since the 18th century, there has been a debate between frequentists and Bayesians. The former insisted that statistical procedures only made sense when one uses the relative frequency concept. The Bayesians supported the use of degrees of belief as a basis for statistical practice.

The frequentist position is the one you probably heard at school: perform an experiment lots of times, and measure the proportion where you get a positive result - this proportion, if you perform the experiment enough times, is the probability.

The problem comes in those cases where we haven't performed an experiment yet, or where there's no possible way an experiment could be performed - in these cases, frequentism can't help us.

In his book Theory of Probability Bruno de Finetti argued that probabilities should be treated as appropriately calibrated degrees of belief, with a one-to-one relationship to betting odds. Using betting as an analogy for all decision-making under uncertainty, he proved that necessary and sufficient conditions for rational betting (i.e. all decision-making under uncertainty) were that subjective degrees of belief satisfied the Kolmogorov axioms for probability. This laid the foundation of an alternative version of probability, now known as Bayesian.

## References

De Finetti, B. The Theory of Probability. Wiley Classics Library. John Wiley and Son. (English translated version, 1973)de:Frequentistischer Wahrscheinlichkeitsbegriff pl:Prawdopodobieństwo obiektywne

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