How Bayes' Theorem Works
Prior Belief
What you believe before seeing any evidence
A balanced prior means you're fairly uncertain. Evidence will have the biggest relative impact here.
Step 1 of 6: Prior Belief
What you believe before seeing any evidence
A balanced prior means you're fairly uncertain. Evidence will have the biggest relative impact here.
Step 2 of 6: Likelihood
How probable is the evidence under each hypothesis?
The evidence is much more likely under H than ¬H. This evidence will strongly boost your belief in the hypothesis.
Step 3 of 6: The Update
Bayes' formula combines prior and likelihood
Evidence boosted belief from 0.30 to 0.659 — a strong upward update because the evidence fits the hypothesis well.
Step 4 of 6: Visual Bayes
An area diagram makes the math intuitive
Both colored areas are comparable. The evidence provides moderate information — neither strongly confirming nor refuting H.
Step 5 of 6: Sequential Updates
Feed evidence one at a time — posteriors compound
Press Play or Step to feed evidence one at a time. Each observation updates your belief — the posterior becomes the next prior.
Step 6 of 6: Bayes in ML
Naive Bayes classification in action
Near the overlap region, both classes are plausible. The decision boundary is where the posterior probabilities cross — this is where uncertainty is highest.