⚖️ Bayesian Inference (2D)

Prior belief P(H): 0.50 Likelihood / sensitivity P(E|H): 0.80 False-positive rate P(E|¬H): 0.20

Prior P(H)0.500

Posterior P(H|E)0.500

Evidence count (n)0

Positive evidence (k)0

Beta shape α, β2.0, 2.0

95% credible interval—

No evidence yet.

Bayes' theorem: P(H|E) = P(E|H)·P(H) / P(E), where P(E) = P(E|H)·P(H) + P(E|¬H)·P(¬H).
Each click runs a genuine Bayesian update on a Beta(α,β) belief distribution over θ = P(H): a positive observation is a "success" (α += 1), a negative observation is a "failure" (β += 1) — the classic Beta-Binomial conjugate update, so the discrete P(H|E) value above and the continuous curve stay exactly consistent.