Difference between revisions of "MediaWiki:Sidebar"
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</tr></table></html> | </tr></table></html> | ||
If | If | ||
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is a | is a | ||
[[Sufficient statistic|sufficient statistic]] | [[Sufficient statistic|sufficient statistic]] | ||
for the family of distributions with densities | for the family of distributions with densities | ||
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then the a posteriori distribution depends not on | then the a posteriori distribution depends not on | ||
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itself, but on | itself, but on | ||
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The asymptotic behaviour of the a posteriori distribution | The asymptotic behaviour of the a posteriori distribution | ||
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as | as | ||
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where | where | ||
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are the results of independent observations with density | are the results of independent observations with density | ||
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is | is | ||
 "almost independent"  |  "almost independent"  | ||
of the a priori distribution of | of the a priori distribution of | ||
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Revision as of 16:38, 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.
todo
Sidebar. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sidebar&oldid=2999