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Difference between revisions of "Bayesian decision function"

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A rule (function) <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015410/b0154101.png" /> which associates with each result <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015410/b0154102.png" /> of a statistical experiment a decision <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015410/b0154103.png" /> with values in a given set of decisions, and which attains the minimum expected loss as defined in the framework of the [[Bayesian approach|Bayesian approach]] to statistical problems.
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A rule (function) $\delta = \delta(x)$ which associates with each result $x$ of a statistical experiment a decision $\delta(x)$ with values in a given set of decisions, and which attains the minimum expected loss as defined in the framework of the [[Bayesian approach|Bayesian approach]] to statistical problems.

Latest revision as of 19:33, 15 February 2013

A rule (function) $\delta = \delta(x)$ which associates with each result $x$ of a statistical experiment a decision $\delta(x)$ with values in a given set of decisions, and which attains the minimum expected loss as defined in the framework of the Bayesian approach to statistical problems.

How to Cite This Entry:
Bayesian decision function. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bayesian_decision_function&oldid=29438
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article