DataTerminology.comNEW
A measure of how much a random sample informs about an unknown parameter, governing estimator variance via the Cramér–Rao bound.
DESCRIPTION
Fisher information quantifies sensitivity of a likelihood to parameter changes, with larger values indicating more informative data. It underpins the Cramér–Rao lower bound, linking information to minimal estimator variance. The Fisher information matrix generalizes to multivariate cases, with its inverse often approximating covariance of maximum likelihood estimators. It is central to statistical inference and experimental design.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistics, the Fisher information is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X.
Directly connects information to parameter inference via likelihood.
Encyclopedia of Mathematics
A numerical characteristic of a family of probability distributions that gives the degree of concentration of the distribution in the vicinity of the true value of a parameter.
Presents information as concentration around the true parameter.
Penn State Eberly College of Science
The Fisher information measures how much information the sample carries about the parameter; larger Fisher information implies a lower bound on variance is smaller.
Explicitly ties Fisher information to variance through the Cramér–Rao bound.
RELATED TERMS
Maximum Likelihood Estimation Cramér–Rao Bound Score Function Information Matrix Estimator Variance Likelihood Observed Information Asymptotic Normality Hessian Confidence Interval
COMPETING TERMS
RELATIONS
- Broader: Information
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist AI Engineer MLOps Engineer Analytics Engineer
EXTERNAL SOURCES
- Wikipedia - Fisher information
- MIT OpenCourseWare - Lecture notes on inference
- Statsmodels - MLE and Fisher information tools
- NIST Engineering Statistics Handbook - Likelihood-based inference overview
TOP QUESTIONS
What is Fisher Information?
It measures how informative a sample is about a parameter, controlling the lower bound of estimator variance via the Cramér–Rao bound.
Category: Definition
How does Fisher Information relate to MLE?
The inverse Fisher information typically approximates the covariance of maximum likelihood estimates under regularity conditions.
Category: Distinction
What is the Fisher Information Matrix?
It generalizes Fisher information to multiple parameters, capturing curvature of the log-likelihood.
Category: Definition
Why is Fisher Information useful in experiment design?
Maximizing information yields lower estimator variance, informing optimal sampling strategies.
Category: Relevancy
How can Fisher Information be computed?
Use the expected squared score or the negative expected Hessian of the log-likelihood.
Category: HowTo
What’s a common misunderstanding about Fisher Information?
Confusing it with Shannon information; Fisher targets parameter estimation, not message entropy.
Category: Misunderstanding
What is the risk of misusing Fisher Information?
Assuming asymptotic approximations in small samples can yield misleading uncertainty estimates.
Category: Risk
Which models benefit most from Fisher Information?
Regular parametric models with well-behaved likelihoods, such as exponential families.
Category: Example
Where do I learn Fisher Information?
Start with Wikipedia, MIT OCW notes, and Penn State online statistics resources, then practice on likelihood-based problems.
Category: Learning