Bayes rules

E766785

Bayesian decision-theoretic concept decision rule statistical decision theory concept

Bayes rules are decision rules in statistical decision theory that minimize expected loss with respect to a prior distribution, forming a central concept in Bayesian optimal decision-making.

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Observed surface forms (1)

Surface form	Occurrences
Bayesian decision theory	5

Statements (48)

Predicate	Object
instanceOf	Bayesian decision-theoretic concept ⓘ decision rule ⓘ statistical decision theory concept ⓘ
appliesTo	classification problems ⓘ hypothesis testing problems ⓘ point estimation problems ⓘ sequential decision problems ⓘ
basedOn	loss function ⓘ posterior distribution ⓘ prior distribution ⓘ
characterizedBy	dependence on prior distribution ⓘ minimization of Bayes risk ⓘ optimality with respect to a specified prior ⓘ
contrastsWith	frequentist decision rules that do not use priors ⓘ
definedAs	decision rules that minimize posterior expected loss with respect to a prior distribution ⓘ
dependsOn	choice of loss function ⓘ choice of prior distribution ⓘ
field	Bayesian statistics NERFINISHED ⓘ decision theory ⓘ statistical decision theory ⓘ
formalizedBy	Abraham Wald NERFINISHED ⓘ Leonard J. Savage NERFINISHED ⓘ
formalizedIn	framework of risk minimization ⓘ
hasExample	Bayesian classifier minimizing expected misclassification loss ⓘ maximum a posteriori (MAP) rule under 0-1 loss ⓘ posterior mean under squared error loss ⓘ posterior median under absolute error loss ⓘ
hasGoal	Bayesian optimal decision-making ⓘ minimize expected loss ⓘ
hasProperty	can be improper if based on improper priors ⓘ can be randomized or non-randomized ⓘ may be non-unique for a given prior and loss function ⓘ often yields admissible rules under regularity conditions ⓘ
historicalContext	developed within the framework of Bayesian decision theory in the 20th century ⓘ
namedAfter	Thomas Bayes NERFINISHED ⓘ
relatedTo	Bayesian estimator NERFINISHED ⓘ admissibility ⓘ complete class theorem ⓘ frequentist risk ⓘ minimax rule ⓘ
subClassOf	admissible decision rule (under mild regularity conditions) ⓘ optimal decision rule ⓘ
usedFor	deriving optimal estimators under Bayesian assumptions ⓘ designing optimal tests under Bayesian criteria ⓘ
usesConcept	Bayes risk NERFINISHED ⓘ posterior expected loss ⓘ prior expected loss ⓘ risk function ⓘ