stats

Bayes' Theorem

Posterior from prior and likelihoods — expanded formula, natural frequency tree, and real-world presets.

Inputs

Prior — P(A) base rate of A

0–1

Likelihood — P(B | A) if A is true, P(B)

0–1

Complement — P(B | ¬A) if A is false, P(B)

0–1

Results

P(B) marginal—

P(A | B) posterior—

P(¬A | B) posterior complement—

Likelihood ratio P(B|A)/P(B|¬A)—

Expanded formula

P(B) = P(B|A)·P(A) + P(B|¬A)·P(¬A)     = ?P(A|B) = P(B|A)·P(A) / P(B)       = ?

P(A|B) = P(B|A)·P(A) / [P(B|A)·P(A) + P(B|¬A)·P(¬A)]