A priori distribution
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.
Comments
References
[a1] | E. Sverdrup, "Laws and chance variations" , 1 , North-Holland (1967) pp. 214ff |
A priori distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=A_priori_distribution&oldid=34101