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A priori distribution

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The probability distribution of a random variable, to be contrasted with the conditional distribution of this random variable under certain additional conditions. Usually the term "a priori distribution" is used in the following way. Let be a pair of random variables (random vectors or more general random elements). The random variable is considered to be unknown, while is considered to be the result of an observation to be used for estimation of . The joint distribution of and is given by the distribution of (now called the a priori distribution) and the set of conditional probabilities of the random variable given . According to the Bayes formula, one can calculate the conditional probability of with respect to (which is now called the a posteriori distribution of ). In statistical problems, the a priori distribution is often unknown (and even the assumption on its existence is not sufficiently founded). For the use of the a priori distribution, see Bayesian approach.


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References

[a1] E. Sverdrup, "Laws and chance variations" , 1 , North-Holland (1967) pp. 214ff
How to Cite This Entry:
A priori distribution. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=A_priori_distribution&oldid=12611
This article was adapted from an original article by Yu.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article