This is the final exam for Bayesian Updating. It pulls together the whole course: the three ingredients — prior, likelihood, posterior — and the move that snaps them together; the medical-test paradox where a positive on a 99%-accurate test still means only about a 9% chance of disease; Bayes’ theorem in full, , plus the odds form you can run on a napkin; the likelihood ratio as a single number for how diagnostic a clue is; and the five ways updating goes wrong. Several questions look easy until you notice the base rate hiding in the numbers, so reason each one through and put a number on it before you answer.
How this exam works
Read carefully — this exam is final. Each question appears one at a time. Once you submit an answer it is locked for good: there’s no going back, no retry, and no restart. Your score is hidden until the end, where you’ll see a pass/fail verdict. The pass mark is 70%. A few questions ask you to select all correct answers.
What is the cleanest one-sentence definition of Bayesian updating?
Select an answer to continue.
Course Recap
Big picture
Bayesian updating, in one picture
- Bayesian Updating
- Prior / Likelihood / Posterior
- Start at the prior, weigh how well evidence fits, land on the posterior — which becomes the next prior
- The medical test
- A positive on a rare disease is mostly a false alarm: ~9%, not 99% — count people, not percentages
- Bayes’ theorem + odds form
- P(H | E) = P(E | H)·P(H) / P(E); or simply prior odds × likelihood ratio = posterior odds
- Likelihood ratio / strength
- LR = P(E | H) / P(E | ¬H); LR = 1 is useless, big LR is strong, and strong evidence must be unlikely under ¬H
- Where updating goes wrong
- Dropping the prior, the inverse fallacy, double-counting, refusing to update, and updating on non-diagnostic evidence
- Prior / Likelihood / Posterior
Key takeaways
Bayesian updating means you never build a belief from scratch. You begin at the prior — usually the base rate — weigh the likelihood (how much more expected the evidence is if your hypothesis is true than if it’s false), and land on a posterior that becomes the prior for the next clue. The medical test is the whole course in one puzzle: a positive on a rare disease is mostly a false alarm — about 9%, not 99% — because the huge healthy crowd’s false positives swamp the tiny sick crowd’s true ones; count people, not percentages, and the paradox dissolves. The full formula and its napkin-friendly twin — prior odds likelihood ratio = posterior odds — are the same theorem; the likelihood ratio is the entire strength of a clue in one number, useless at and powerful only when far from it (which is why extraordinary claims require extraordinary evidence — a tiny prior needs a huge ratio to overcome). And the five ways it all goes wrong are worth memorizing: dropping the prior, the inverse fallacy, double-counting correlated evidence, refusing to update, and updating on non-diagnostic evidence. Start from your prior, then move exactly as far as the evidence — no further.