# Bayes Lab

Canonical: https://manyspace.aporia.systems/tools/bayes
Updated: 2026-10-13

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.

## 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.

## Related tools

- [Derivative Visualizer](https://manyspace.aporia.systems/tools/derivative)
- [Integral Explorer](https://manyspace.aporia.systems/tools/integral)
- [Unit Circle Explorer](https://manyspace.aporia.systems/tools/unit-circle)
- [Complex Plane Explorer](https://manyspace.aporia.systems/tools/complex-plane)
- [Probability Lab](https://manyspace.aporia.systems/tools/probability)
- [Eigen Explorer](https://manyspace.aporia.systems/tools/eigenvectors)
- [Fourier Series](https://manyspace.aporia.systems/tools/fourier-series)