Jeffreys prior

E765761

noninformative prior objective Bayesian prior prior distribution

Jeffreys prior is an objective Bayesian prior distribution defined to be invariant under reparameterization by constructing it from the square root of the determinant of the Fisher information matrix.

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Statements (48)

Predicate	Object
instanceOf	noninformative prior ⓘ objective Bayesian prior ⓘ prior distribution ⓘ
appliesTo	parametric statistical models ⓘ
basedOn	Fisher information matrix NERFINISHED ⓘ
canYield	proper posterior under suitable conditions ⓘ
contrastedWith	subjective prior ⓘ uniform prior ⓘ
definedAs	prior with density proportional to the square root of the determinant of the Fisher information matrix ⓘ
dependsOn	likelihood function ⓘ sampling distribution ⓘ
exampleFor	Bernoulli parameter ⓘ Poisson rate parameter ⓘ normal mean with known variance ⓘ normal variance with known mean ⓘ
field	Bayesian statistics ⓘ statistics ⓘ
gives	Beta(1/2, 1/2) prior for Bernoulli success probability ⓘ Gamma(1/2, 0) improper prior for Poisson rate ⓘ uniform prior on the real line for normal mean with known variance ⓘ π(σ²) ∝ 1/σ² for normal variance with known mean ⓘ
hasAdvantage	invariance under one-to-one reparameterizations ⓘ
hasAlternative	Bernardo–Berger reference prior NERFINISHED ⓘ maximum entropy prior ⓘ
hasForm	π(θ) ∝ √I(θ) for one-dimensional parameter θ ⓘ π(θ) ∝ √det(I(θ)) for multidimensional parameter θ ⓘ
hasLimitation	can be difficult to compute for complex models ⓘ may be improper in some models ⓘ may not reflect substantive prior knowledge ⓘ
hasProperty	coordinate invariance ⓘ reparameterization invariance ⓘ
introducedBy	Harold Jeffreys NERFINISHED ⓘ
introducedIn	20th century ⓘ
isSpecialCaseOf	reference prior concepts ⓘ
mayBe	improper prior ⓘ
motivatedBy	desire for objective Bayesian procedures ⓘ principle of parameterization invariance ⓘ
namedAfter	Harold Jeffreys NERFINISHED ⓘ
relatedTo	Fisher information NERFINISHED ⓘ information geometry ⓘ invariant measures ⓘ reference priors ⓘ
usedFor	hypothesis testing ⓘ model comparison ⓘ parameter estimation ⓘ
usedIn	Bayes factor computation ⓘ objective Bayesian analysis ⓘ objective model selection ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Fisher information → relatedTo → Jeffreys prior ⓘ

Fisher information → usedToDefine → Jeffreys prior ⓘ

Harold Jeffreys → knownFor → Jeffreys prior ⓘ