Bayes optimality
E766787
Bayes optimality is a criterion in statistical decision theory under which a decision rule minimizes expected loss with respect to a given prior distribution, making it the benchmark for comparing and justifying optimal procedures.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
concept in Bayesian statistics
ⓘ
concept in statistical decision theory ⓘ decision-theoretic criterion ⓘ |
| appliesTo |
classification
ⓘ
hypothesis testing ⓘ point estimation ⓘ prediction ⓘ |
| assumes | specified prior over unknown parameters ⓘ |
| basedOn | Bayes risk minimization NERFINISHED ⓘ |
| benchmarkFor |
comparing statistical decision rules
ⓘ
justifying optimal procedures ⓘ |
| characterizedBy |
dependence on a specified prior distribution
ⓘ
minimization of posterior expected loss ⓘ |
| contrastedWith |
admissibility
ⓘ
minimax optimality ⓘ |
| criterionFor |
decision rule
ⓘ
statistical procedure ⓘ |
| definedAs | property of a decision rule that minimizes expected loss with respect to a prior distribution ⓘ |
| dependsOn |
choice of loss function
ⓘ
choice of prior distribution ⓘ |
| evaluatedBy | Bayes risk functional ⓘ |
| field |
Bayesian statistics
ⓘ
statistical decision theory ⓘ |
| formalizedIn | modern decision theory ⓘ |
| goal | minimize Bayes risk ⓘ |
| historicalRoot | work of Thomas Bayes ⓘ |
| implies | no other decision rule has lower expected loss under the given prior ⓘ |
| influences |
design of Bayesian classifiers
ⓘ
design of Bayesian estimators ⓘ |
| invariantUnder | equivalent reparameterizations of the model (given transformed prior and loss) ⓘ |
| mathematicalNature | optimization problem over decision rules ⓘ |
| relatedTo |
Bayes classifier
NERFINISHED
ⓘ
Bayes estimator ⓘ Bayes rule NERFINISHED ⓘ |
| requires |
probabilistic model for data
ⓘ
specification of action space ⓘ |
| typicalAssumption | rational decision maker minimizing expected loss ⓘ |
| usedIn |
econometrics
ⓘ
machine learning ⓘ pattern recognition ⓘ signal processing ⓘ |
| usesConcept |
Bayes risk
NERFINISHED
ⓘ
expected loss ⓘ loss function ⓘ prior distribution ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.