Bayesian Odds, Likelihood Ratios, and Base-Rate Traps

Free SOA Exam P (Probability) lesson in General Probability. 16 min read, ~2,447 words.

Odds form of Bayes: posterior odds = prior odds likelihood ratio. One multiplication updates a belief, with no total-probability denominator. Likelihood ratio:. For a positive test, that is sensitivity over. Negative result: carries its own, usually well below 1, dragging the posterior below the base rate. Odds to probability: if...