Namespaces
Variants
Actions

Difference between revisions of "MediaWiki:Sidebar"

From Encyclopedia of Mathematics
Jump to: navigation, search
Line 52: Line 52:
 
in the theory of statistical decisions, see
 
in the theory of statistical decisions, see
 
[[Bayesian approach|Bayesian approach]].
 
[[Bayesian approach|Bayesian approach]].
 +
 +
====References====
  
 
todo
 
todo

Revision as of 16:54, 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

<html>

</html>

If <html></html> is a sufficient statistic for the family of distributions with densities <html>, then the a posteriori distribution depends not on itself, but on . The asymptotic behaviour of the a posteriori distribution as , where are the results of independent observations with density ,</html> is  "almost independent"  of the a priori distribution of <html></html>.


For the role played by a posteriori distributions in the theory of statistical decisions, see Bayesian approach.

References

todo

How to Cite This Entry:
Sidebar. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sidebar&oldid=3000