bayes-as-updating

Bayes' theorem isn't really about probability. It's about how to update beliefs in light of evidence.

Start with a prior — what you believed before. See evidence. The posterior is your new belief, weighted by how surprising the evidence would be under each hypothesis.

The mistake people make: treating their prior as if it were the truth. The mistake people also make: throwing away the prior because new evidence arrived.

Good thinking is calibrated updating. It is also rare.