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 16:07, 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
How to Cite This Entry:
Sidebar. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sidebar&oldid=2987
Sidebar. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sidebar&oldid=2987