---
tag: P944X6S117
kind: concept
name: Bayesian hierarchical model
msc: [62F15]
specializes: [K3AMMSY8DD]
sources:
  - url: https://en.wikipedia.org/wiki/Bayesian_hierarchical_modeling
same_as:
  wikidata: Q17100952
  wikipedia: Bayesian hierarchical modeling
---

## Summary

A Bayesian hierarchical model specifies a [[prior|00NBBSXRQS]] in several stages.
The parameters of the data model have a prior, and that prior has unknown hyperparameters with their own hyperprior.
It describes data in related groups, whose parameters are different but drawn from a common population.
Its [[posterior|0KJ7ZS8AJA]] lets groups borrow strength from each other, and it is a fully Bayesian counterpart of the [[empirical Bayes method|8GG2Z2E61R]].

## Explanations

### L1 human

Think of test scores in many schools.
Each school has its own average level, but the schools are alike in many ways.
A hierarchical model says: each school's level comes from a common distribution of levels, and the shape of that distribution is itself unknown.
A small school with few scores then gets an estimate pulled towards the overall average, while a large school mostly keeps its own average.