---
tag: 605M5NMFD5
kind: concept
name: Identifiability
msc: [62A01, 62F99]
sources:
  - url: https://en.wikipedia.org/wiki/Identifiability
same_as:
  wikidata: Q1656753
  wikipedia: Identifiability
---

## Summary

A [[statistical model|K3AMMSY8DD]] is identifiable when different parameter values give different laws of the data.
Then the law of the data determines the parameter, and it makes sense to estimate the parameter.
Without identifiability no amount of data can separate parameters that give the same law, and consistent estimation of them is impossible.

## Explanations

### L1 human

Imagine that you see only the sum of two unknown numbers plus some noise.
You can learn the sum, but you can never learn the two numbers apart, since $1 + 2$ and $2 + 1$ give the same data.
Such a model is not identifiable.
In an identifiable model each parameter value leaves its own fingerprint on the distribution of the data.