Fisher information
E212219
Fisher information is a fundamental concept in statistics that quantifies how much information an observable random variable carries about an unknown parameter, playing a key role in estimation theory and the Cramér–Rao bound.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Fisher information canonical | 2 |
| Fisher information inequality | 1 |
| Fisher information matrix | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1908298 — 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: Fisher information Context triple: [Ronald A. Fisher, knownFor, Fisher information]
-
A.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
-
B.
Chernoff information
Chernoff information is a measure in information theory and statistics that quantifies the exponential rate at which the error probability decays when optimally distinguishing between two probability distributions.
-
C.
Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
-
D.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
E.
Rényi divergence
Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
- 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: Fisher information Target entity description: Fisher information is a fundamental concept in statistics that quantifies how much information an observable random variable carries about an unknown parameter, playing a key role in estimation theory and the Cramér–Rao bound.
-
A.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
-
B.
Chernoff information
Chernoff information is a measure in information theory and statistics that quantifies the exponential rate at which the error probability decays when optimally distinguishing between two probability distributions.
-
C.
Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
-
D.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
E.
Rényi divergence
Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
information measure
ⓘ
statistical concept ⓘ |
| appearsIn |
Cramér–Rao bound
ⓘ
surface form:
Cramér–Rao inequality
|
| appliesTo | parametric statistical models ⓘ |
| assumes | regularity conditions for interchange of differentiation and expectation ⓘ |
| context |
Bayesian statistics
ⓘ
frequentist statistics ⓘ |
| definedAs |
expected value of the squared derivative of the log-likelihood with respect to the parameter
ⓘ
negative expected value of the second derivative of the log-likelihood with respect to the parameter ⓘ variance of the score function ⓘ |
| dependsOn |
parameter θ
ⓘ
probability distribution of the data ⓘ |
| field |
estimation theory
ⓘ
information theory ⓘ statistics ⓘ |
| hasForm |
matrix (Fisher information matrix) for multidimensional parameter
ⓘ
scalar quantity for one-dimensional parameter ⓘ |
| hasInterpretation | Riemannian metric on statistical manifolds ⓘ |
| introducedBy | Ronald A. Fisher ⓘ |
| namedAfter | Ronald A. Fisher ⓘ |
| property |
additive for independent observations
ⓘ
invariant under reparameterization up to chain rule ⓘ nonnegative ⓘ |
| quantifies | amount of information an observable random variable carries about an unknown parameter ⓘ |
| relatedConcept |
expected information
ⓘ
observed information ⓘ |
| relatedTo |
Jeffreys prior
ⓘ
Kullback–Leibler divergence ⓘ asymptotic normality of maximum likelihood estimators ⓘ information geometry ⓘ score function ⓘ |
| role |
characterizes efficiency of estimators
ⓘ
measures local sensitivity of likelihood to parameter changes ⓘ provides lower bound on variance of unbiased estimators ⓘ |
| symbol | I(θ) ⓘ |
| timePeriod | 1920s ⓘ |
| usedFor |
computing standard errors of estimators
ⓘ
constructing confidence intervals ⓘ optimal experimental design via information maximization ⓘ |
| usedIn |
Cramér–Rao bound
ⓘ
asymptotic theory of estimators ⓘ experimental design ⓘ hypothesis testing ⓘ maximum likelihood estimation ⓘ parameter estimation ⓘ |
| usedToApproximate | curvature of the log-likelihood function at the true parameter ⓘ |
| usedToDefine |
Jeffreys prior
ⓘ
natural gradient in information geometry ⓘ |
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: Fisher information Description of subject: Fisher information is a fundamental concept in statistics that quantifies how much information an observable random variable carries about an unknown parameter, playing a key role in estimation theory and the Cramér–Rao bound.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Fisher information matrix
this entity surface form:
Fisher information inequality