Bayes in Plain Words

Bayes’ rule is a way of changing your mind in proportion to the evidence. You begin with a starting belief: how likely the claim was before the new fact. Then you ask how much more likely that fact is if the claim is true than if it is false.

If a fact is much more likely under the claim, your belief should rise a lot. If it is about equally likely either way, your belief should barely move. A strong-sounding fact that fits both stories tells you little.

The rule guards against two habits: ignoring the starting belief, and treating any one fact as final. Each new fact nudges your belief up or down, and the size of the nudge depends on how well it fits each story.

The late friend

Eve’s friend Jo is usually on time. Tonight Jo is twenty minutes late. Eve wonders whether Jo forgot. Starting belief: Jo rarely forgets, so she thinks it unlikely.

Eve asks how likely this lateness is if Jo forgot, and how likely if Jo hit traffic. Both are plausible, so her belief moves only a little. When Jo texts “stuck on the bridge,” which fits traffic far better, she drops the forgot idea.

Try this today Pick a belief, say how sure you were, and write how much one new fact should move it.