Jeffreys prior
E765761
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Jeffreys prior canonical | 3 |
| Jeffreys prior (via volume element) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8912633 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Jeffreys prior Context triple: [Fisher information, relatedTo, Jeffreys prior]
-
A.
Bayes factor
The Bayes factor is a Bayesian model comparison metric that quantifies how much more strongly data support one statistical model or hypothesis over another.
-
B.
Bayes’ theorem
Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
-
C.
Dirichlet distribution
The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
-
D.
Bayesian inference
Bayesian inference is a statistical framework that updates the probability of hypotheses as more evidence or data becomes available, using Bayes’ theorem to combine prior beliefs with observed information.
-
E.
Bayesian Occam factor
The Bayesian Occam factor is a term in Bayesian model comparison that automatically penalizes overly complex models by integrating over their larger parameter spaces, thereby implementing Occam’s razor in probabilistic inference.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Jeffreys prior Target entity description: 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.
-
A.
Bayes factor
The Bayes factor is a Bayesian model comparison metric that quantifies how much more strongly data support one statistical model or hypothesis over another.
-
B.
Bayes’ theorem
Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
-
C.
Dirichlet distribution
The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
-
D.
Bayesian inference
Bayesian inference is a statistical framework that updates the probability of hypotheses as more evidence or data becomes available, using Bayes’ theorem to combine prior beliefs with observed information.
-
E.
Bayesian Occam factor
The Bayesian Occam factor is a term in Bayesian model comparison that automatically penalizes overly complex models by integrating over their larger parameter spaces, thereby implementing Occam’s razor in probabilistic inference.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
noninformative prior
ⓘ
objective Bayesian prior ⓘ prior distribution ⓘ |
| appliesTo | parametric statistical models ⓘ |
| basedOn |
Fisher information matrix
ⓘ
linked to:
Fisher information
|
| 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
ⓘ
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 ⓘ |
| introducedIn | 20th century ⓘ |
| isSpecialCaseOf | reference prior concepts ⓘ |
| mayBe | improper prior ⓘ |
| motivatedBy |
desire for objective Bayesian procedures
ⓘ
principle of parameterization invariance ⓘ |
| namedAfter | Harold Jeffreys ⓘ |
| relatedTo |
Fisher information
ⓘ
information geometry ⓘ invariant measures ⓘ reference priors ⓘ |
| usedFor |
hypothesis testing
ⓘ
model comparison ⓘ parameter estimation ⓘ |
| usedIn |
Bayes factor computation
ⓘ
objective Bayesian analysis ⓘ objective model selection ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Jeffreys prior Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Jeffreys prior