Prior Probability¶
Summary¶
The probability of a hypothesis before considering new evidence — the starting point that Bayesian reasoning updates when evidence arrives.
Definition¶
In Bayes' theorem: P(H) — the probability that hypothesis H is true before seeing any evidence.
Why It Matters¶
The prior represents your base rate — the frequency of something in the general population. Ignoring it leads to the base rate fallacy.
Classic Examples¶
Steve the Librarian¶
- Prior: 1 in 21 chance Steve is a librarian (based on 20:1 farmer-to-librarian ratio)
- This prior is crucial — even strong evidence (4× more likely to be a librarian given the description) can't overcome a weak prior
Breast Cancer Screening¶
- Prior: 1% chance a random woman has breast cancer
- After positive mammogram: posterior becomes 25%
- The low prior means most positive results are false positives
Determining the Prior¶
The prior depends on context and assumptions: - Is Steve a randomly sampled American? (20:1 farmer:librarian) - Is Steve someone you personally know? (your personal ratio may differ) - "Rationality is not about knowing facts — it's about recognizing which facts are relevant." — Grant Sanderson
The Geometric View¶
In the 1×1 square diagram, the prior is the width of the hypothesis portion — how much of the total possibility space the hypothesis occupies before evidence narrows it down.
Common Mistakes¶
- Ignoring the prior — focusing only on likelihoods (evidence strength)
- Setting the prior too high — assuming rare events are common
- Setting the prior to 0 or 1 — making beliefs unchangeable regardless of evidence
- Not thinking about the reference class — which population to draw the prior from