P(H) — Prior
P(H̄)
P(E|H) true positive
P(E|H̄) false positive
P(H|E) posterior
Scenarios
Parameters
—
P(H|E) — Posterior
P(H|E) =
P(E|H) × P(H)
──────────────────────
P(E|H)·P(H) + P(E|H̄)·P(H̄)
──────────────────────
P(E|H)·P(H) + P(E|H̄)·P(H̄)
Base rate fallacy: Even a 99% accurate test for a 1% disease gives only ~17% posterior probability — most positives are false!
P(E) = P(E|H)P(H) + P(E|H̄)P(H̄)
The area diagram shows exactly which fraction of the "positive evidence" box comes from true vs. false positives.
P(E) = P(E|H)P(H) + P(E|H̄)P(H̄)
The area diagram shows exactly which fraction of the "positive evidence" box comes from true vs. false positives.