# Difference between revisions of "MediaWiki:Sidebar"

From Encyclopedia of Mathematics

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[[A priori distribution|a priori distribution]]. | [[A priori distribution|a priori distribution]]. | ||

− | + | Let | |

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100301.png"> | ||

+ | be a random parameter with an a priori density | ||

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100302.png">, | ||

+ | let | ||

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100303.png"> | ||

+ | be a random result of observations and let | ||

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100304.png"> | ||

+ | be the conditional density of | ||

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100305.png"> | ||

+ | when | ||

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100306.png">; | ||

+ | then the a posteriori distribution of | ||

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100307.png"> | ||

+ | for a given | ||

+ | <img align="absmiddle" border="0" src="images/a010/a010030/a0100308.png">, | ||

+ | according to the | ||

+ | <a href="../b/b015380.htm">Bayes formula</a>, | ||

+ | has the density | ||

todo | todo |

## Revision as of 18:07, 16 June 2010

A conditional probability distribution of a random variable, to be contrasted with its unconditional or a priori distribution.

Let be a random parameter with an a priori density , let be a random result of observations and let be the conditional density of when ; then the a posteriori distribution of for a given , according to the <a href="../b/b015380.htm">Bayes formula</a>, has the density

todo

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*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Sidebar&oldid=2988