---
tag: 21JT983G60
kind: concept
name: Bayesian network
msc: [62H22, 68T37]
specializes: [Q3FQAD1BXG]
sources:
  - url: https://en.wikipedia.org/wiki/Bayesian_network
same_as:
  wikidata: Q812540
  wikipedia: Bayesian network
---

## Summary

A Bayesian network is a [[graphical model|Q3FQAD1BXG]] on a directed acyclic graph.
The joint distribution is the product of the conditional distributions of each variable given its parents in the graph.
The arrows can often be read as direct influences, which makes Bayesian networks a common language for reasoning under uncertainty and for [[causal inference|V3QJFN5800]].
Efficient algorithms compute conditional probabilities in networks with sparse graphs.

## Explanations

### L1 human

Rain makes the grass wet, and so does the sprinkler; rain also makes it less likely that the sprinkler is on.
Draw an arrow from each cause to each thing it directly affects, with no loops of arrows.
Then give, for each variable, its probabilities for every combination of its causes.
These small tables together fix the probability of every full scenario, as their product.