Bayes Lab
A 95%-accurate test can still cry wolf 5 times out of 6. The crowd decides what a positive means — move the prior and watch.
Tip: park sensitivity and false alarms, then drag the prior from 1% to 30%.
Try this
- Flip the crowd. Jump from Rare defect to Common trait without touching the test: the same positives go from 16% to 89% meaningful.
- Break the test. Pick Sloppy test and push the false-positive rate up: watch the verdict sink even though the test still “works”.
- Empty the board. Drop the prior, sensitivity, and false alarms to zero: with no positives, “given a positive” has no answer — the honest edge of the rule.
How to read the three bars
Bar one is the crowd, split by truth. Bar two is everyone the test flags — true positives in bright, false alarms striped. Bar three zooms into those positives alone: its bright fraction is the posterior, P(defect | +).
The formula says the same thing — posterior = sensitivity × prior / P(positive) — but the bars show why the prior dominates: when defects are rare, even a small false-positive rate harvests far more healthy widgets than the test finds defective ones.
Base rates run the world
Tests, trials, and predictions all answer to the prior — ManySpace teaches probability the way you just touched it: crowds first, formulas second.