---
title: "Bayesian network"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "Bayesian network"
aliases: ["Bayesian networks","belief network","Bayes network"]
first_seen: "2026-07-11T00:00:00.000Z"
writer_model: "warden/claude-opus-4.8"
connects_to: ["probabilistic graphical models","certainty factors","Judea Pearl","expert systems","statistical inference"]
seek_code_commit: "b13747c"
---


A Bayesian network is a directed graphical model that represents a set of
variables and their conditional dependencies as a graph, and updates beliefs by
propagating probabilities across it. [[entity-judea-pearl|Judea Pearl]] proposed
the belief-updating algorithm in a 1982 paper ("Reverend Bayes on Inference
Engines") and named the approach "Bayesian networks" by 1985, explicitly to give
uncertain reasoning "coherence with orthodox probability theory and Bayesian
reasoning" — the property he argued the ad hoc combination rules of 1970s expert
systems lacked.

In this vault the concept is load-bearing as the **destination** of a recurring
historical pattern: an AI heuristic method, built on hand-tuned uncertainty
arithmetic, is later rebuilt on Bayesian-network statistical inference. It is the
constructive answer to the certainty-factor scheme of
[[claim-mycin-certainty-factors-non-bayesian-uncertainty|MYCIN]] — the scheme
[[claim-heckerman-1986-certainty-factors-require-independence-assumptions|Heckerman
proved incoherent]] and [[claim-pearl-built-bayesian-networks-as-coherent-alternative-to-certainty-factors|Pearl
replaced]] — and it recurs, independently, as the formalism two unrelated
communities reached for when they finally made their heuristics rigorous:
medical diagnosis (the Pathfinder project) and intelligence analysis (Heuer's
Analysis of Competing Hypotheses). The pattern is why the vault treats the two
senses of "inference" (the classic expert-system engine vs. statistical
inference over a distribution) as a genuine connection here rather than a shared
word — the bridge is documented, not cosine-deep.

## References
- [[claim-pearl-built-bayesian-networks-as-coherent-alternative-to-certainty-factors]] — Pearl's own account: built for probabilistic coherence, motivated by the certainty-factor scheme's failure on "explaining away."
- [[claim-pathfinder-rebuilt-from-rules-to-bayesian-networks]] — the empirical case in medical diagnosis: a lymph-node pathology system carried from rule-chaining to probabilistic scoring, the expert's blind verdict of improvement landing at the simple-Bayes step.
- [[claim-valtorta-reformulated-ach-as-bayesian-networks]] — the second, independent domain: an intelligence-funded CS group recast ACH as Bayesian networks, not as rule-chaining.
- [[claim-heckerman-1986-certainty-factors-require-independence-assumptions]] — the critique that motivates the replacement: certainty factors are coherent only under hidden independence assumptions.
- [[claim-mycin-certainty-factors-non-bayesian-uncertainty]] — the predecessor scheme the concept is defined against.