Bayesian vs. frequentist?

Frequentists treat probability as long-run frequency; Bayesians treat it as degree of belief.

Any tip for doing it in your head?

Convert percentages into natural frequencies, like "out of 1,000 people."

Bayes' Theorem

➗ Mathematics & Statistics By CampusDown Wiki Editorial Team Last updated October 26, 2026

Bayes' theorem is a conditional-probability formula for updating a prior belief into a posterior belief when new evidence comes in.

Contents

1. What does the formula mean?
2. Does a positive test mean you're sick?
3. FAQ
4. References

What does the formula mean?

P(A) is the prior—your belief before seeing evidence. P(B|A) is the likelihood of the evidence if A is true. P(A|B) is the posterior, your updated belief. In short: posterior ∝ likelihood × prior. Each new piece of evidence updates what you believe.

Does a positive test mean you're sick?

Say a disease affects 1% of people and a test catches 90% of cases with a 9% false-positive rate. Out of 1,000 people, 9 of the 10 sick test positive—but so do about 89 of the 990 healthy. So a positive result means only about 9/98 ≈ 9% chance of disease. Ignoring the prior is the base rate fallacy. The same logic powers spam filters and naive Bayes classifiers.

FAQ

Bayesian vs. frequentist?: Frequentists treat probability as long-run frequency; Bayesians treat it as degree of belief.
Any tip for doing it in your head?: Convert percentages into natural frequencies, like "out of 1,000 people."

Sources reviewed: 2026-10-25

References

Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions, 53, 370–418.
Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction. Psychological Review, 102(4), 684–704.

Reports and materials that use this theory (Korean)

There are no materials dedicated to this theory yet, but you can search related reports in the CampusDown library (Korean).

Find more reports · Search '베이즈 정리' on CampusDown →

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This article was last updated on October 26, 2026. It is based on widely recognized original works and textbooks; when citing it in a paper, please check the original sources listed in the references.