Statistics › Section N · Counting, Bayesian inference, and multiple regression › Topic N.2
Bayes' theorem as learning from evidence
Swapping P(positive | disease) for P(disease | positive) is one of the commonest errors in probability. Bayes' theorem is the correct way to make that reversal: a rule for turning evidence into updated belief, one observation at a time.
In this topic
- The reversal the fallacy needs
- Prior, likelihood, posterior
- Bayes' theorem, exactly
- Worked example: the medical test, reversed properly
- Worked example: evidence accumulates
- The odds form
- Choosing priors honestly
- Sequential updating everywhere
- Common mistakes to avoid
- Key takeaways
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