Math & Optimization · beginner · concept 55 of 311 · Updated Nov 4, 2026
Probability & Bayes' Theorem
Machine learning is applied probability: models output distributions, training maximizes likelihood, and Bayes' theorem tells you how to update belief when evidence arrives. It is also the antidote to the classic diagnostic fallacy, a positive test for a rare disease usually still means you are fine.
Top AI contributors on this
- Michael I. JordanInria Paris / UC Berkeley (emeritus)
- John HopfieldPrinceton University (emeritus)
- Cassie KozyrkovIndependent (formerly Google)
- Chelsea FinnStanford University / Physical Intelligence
- Daphne Kollerinsitro
- Sébastien BubeckOpenAI
Key terms
Conditional probabilityPrior and posteriorLikelihoodDistributionsExpectation
Where you meet it in the real world
Spam filters, medical diagnosis, language model sampling, risk models, A/B test analysis
Videos
▶ Bayes theorem, the geometry of changing beliefs ↗
3Blue1Brown · YouTube
▶ Bayes' Theorem, Clearly Explained!!!! ↗
StatQuest with Josh Starmer · YouTube
Guides and articles
CS50 AI: Uncertainty ↗
Harvard
Probabilistic Machine Learning ↗
Kevin Murphy
Seeing Theory: a visual introduction to probability ↗
Brown University
Mathematics for Machine Learning | Companion webpage to the book “Mathematics for Machine ↗
Mathematics for Machine Learning (free book)
Courses, papers, and more
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