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[[A priori distribution|a priori distribution]].
 
[[A priori distribution|a priori distribution]].
  
 
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Let
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<img align="absmiddle" border="0" src="images/a010/a010030/a0100301.png">
 +
be a random parameter with an a priori density
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<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
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<img align="absmiddle" border="0" src="images/a010/a010030/a0100304.png">
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be the conditional density of
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<img align="absmiddle" border="0" src="images/a010/a010030/a0100305.png">
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when
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<img align="absmiddle" border="0" src="images/a010/a010030/a0100306.png">;
 +
then the a posteriori distribution of
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<img align="absmiddle" border="0" src="images/a010/a010030/a0100307.png">
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for a given
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<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

How to Cite This Entry:
Sidebar. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Sidebar&oldid=2988