quantity

fisher information

A measure of the amount of information an observable random variable carries about an unknown parameter, used to quantify sensitivity.
5 related articles

Description

Fisher information is a concept from statistics and information theory that quantifies how much information an observable random variable provides about an unknown parameter. It measures the sensitivity of the probability distribution to changes in that parameter. If a small change in the parameter causes a large shift in the likelihood of observed data, the Fisher information is high; if the data barely changes, it is low.

History

Introduced by Ronald Fisher in the 1920s as part of his foundational work on maximum likelihood estimation.

How it works

Formally, it is the variance of the score, which is the derivative of the log-likelihood with respect to the parameter. For a given probability distribution, the Fisher information is a single number (or a matrix for multiple parameters) that sets a lower bound on the variance of any unbiased estimator, known as the Cramér–Rao bound. This makes it a fundamental tool for assessing the precision of statistical estimates.

In practice

It is used in experimental design to optimize measurements, in quantum metrology to achieve precision beyond classical limits, and in machine learning for parameter estimation.

Fun fact

In quantum mechanics, the Fisher information is related to the speed of evolution of a quantum state, linking statistics to the Heisenberg uncertainty principle.

Related articles · 5

Quantum Physics2026-05-012 minarXiv:2605.00770express
Topology Holds Memory
A drop of ink falls into a glass of water, and within a minute you can't tell where it landed. In the quantum world, it's even more dramatic: information about a local event spreads across the entire system so quickly that any point-like sensor soon stops feeling anything. This is called delocalization, and for quantum sensors, it sounds like a death sentence.
Geophysics2026-03-161 minarXiv:2603.14844express
The Ocean Listens Through Fiber Optics
Thousands of kilometers of fiber-optic cables lie on the ocean floor. They carry internet traffic, but the cables themselves sense the slightest vibrations in the water and the seabed. If you listen closely to such a cable, you can hear a blue whale singing or the ground trembling thousands of kilometers away.
Getting the Most Out of Every Photon
A fluorescence microscope is like a photographer shooting in the dark: the more frames, the better the view, but each frame costs photons. In a living cell, the supply is limited, otherwise the light would simply kill the sample. So scientists proposed not to increase the number of photons, but to choose more wisely when to catch them.
Quantum Physics2025-12-161 minarXiv:2512.14899express
Precision of Quantum Sensors: An Unexpected Twist
Building ultrasensitive sensors for light measurements and spectroscopy starts with tiny chambers where light ricochets like an echo in a canyon. Previously, engineers chased the quality factor — the duration of this echo: the longer it rings, the more noticeable the slightest changes.
A Sieve for Nature: How IMPIT Indices Sift Important Episodes from Noisy Signals
A fisherman in Queensland notices that in some years snapper are harder to catch, even though the nets and boat are the same. The reason hides not in the catch itself but in the water temperature several months earlier, when the fry were just hatching. A warm current arrived not for the whole year but only for a few weeks, and that short episode decided the fate of an entire fish generation.