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Difference between revisions of "MediaWiki:Sidebar"

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in the theory of statistical decisions, see
 
in the theory of statistical decisions, see
 
[[Bayesian approach|Bayesian approach]].
 
[[Bayesian approach|Bayesian approach]].
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====References====
  
 
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Revision as of 18:54, 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

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How to Cite This Entry:
Sidebar. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Sidebar&oldid=3001