---
tag: 8GG2Z2E61R
kind: concept
name: Empirical Bayes method
msc: [62C12, 62F15]
sources:
  - url: https://en.wikipedia.org/wiki/Empirical_Bayes_method
same_as:
  wikidata: Q5374241
  wikipedia: Empirical Bayes method
---

## Summary

An empirical Bayes method estimates the [[prior distribution|00NBBSXRQS]] from the data and then uses it as if it were known.
It applies when many similar parameters are estimated at once, so that the data on all of them show how the parameters are spread.
It sits between full [[Bayesian inference|0JWRJX2RMP]] and frequentist estimation, and it explains shrinkage estimators such as the [[James–Stein estimator|709T196XCT]].

## Explanations

### L1 human

Suppose you rate a thousand baseball players, each from a short season.
Each player's own average is noisy, but the thousand averages together show how batting skill is spread in the league.
Empirical Bayes uses that spread as a prior and pulls each player's average a bit towards the league average.
The pull is strong for players with little data and weak for players with a lot of data.