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Let
 
Let
<img align="absmiddle" border="0" src="images/a010/a010030/a0100301.png" />
+
<html><img align="absmiddle" border="0" src="images/a010/a010030/a0100301.png">
 
be a random parameter with an a priori density
 
be a random parameter with an a priori density
 
<img align="absmiddle" border="0" src="images/a010/a010030/a0100302.png">,
 
<img align="absmiddle" border="0" src="images/a010/a010030/a0100302.png">,
Line 18: Line 18:
 
<img align="absmiddle" border="0" src="images/a010/a010030/a0100307.png">
 
<img align="absmiddle" border="0" src="images/a010/a010030/a0100307.png">
 
for a given
 
for a given
<img align="absmiddle" border="0" src="images/a010/a010030/a0100308.png">,
+
<img align="absmiddle" border="0" src="images/a010/a010030/a0100308.png"></html>,
 
according to the
 
according to the
<a href="../b/b015380.htm">Bayes formula</a>,
+
[[Bayes formula|Bayes formula]],
 
has the density
 
has the density
  

Revision as of 17:20, 16 June 2010

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

Let <html> 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 </html>, according to the Bayes formula, has the density


todo

How to Cite This Entry:
Sidebar. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Sidebar&oldid=2990