Appendix A — Bayes in One Page

Appendix A — Bayes in One Page

You do not need the equation to use the idea. You need three questions, always asked in order.

**1. The prior — how likely was it before I saw anything?** Start with the base rate. Of all the people / cases / situations like this, how often is my hypothesis actually true, in general? Write down a rough number. This is the floor. Ignore it and everything else collapses.

**2. The likelihood — how well does the clue fit, compared to the alternatives?** Ask two questions, not one. If my hypothesis were true, how expected is this clue? And — the one amateurs forget — if my hypothesis were false, how expected is this clue anyway? A clue is only worth something to the degree it fits your theory better than it fits the rivals. A clue every explanation predicts equally is worthless, however vivid.

3. The posterior — so where does that leave me? Combine them. A strong clue on top of a tiny prior still usually lands on a small number (remember the disease test: a 95%-accurate positive still meant a ~2% chance of illness, because the disease was rare). Update toward your hypothesis by an amount proportioned to how much better the clue fits it than the alternatives — then stop, and hold the result loosely.

The one-sentence version: A clue should move your belief in proportion to how much more likely it makes your explanation than the others — starting from how likely that explanation was to begin with. Everything else is bookkeeping.

The worked example to keep in your pocket: disease in 1 of 1,000; test catches ~all real cases but false-alarms 5% of the time. Out of 100,000 people: ~100 true positives, ~5,000 false alarms. A positive result → about 100 in 5,100 ≈ 2%. The vivid clue lost to the boring base rate. It almost always does.