Predicting the Future with Bayes' Theorem
Farnam Street (Shane Parrish), after Thomas Bayes · 2022
"Good judgment under uncertainty means continuously updating your probability estimates as new evidence arrives, weighting that new evidence against what you already knew (your 'priors') rather than either ignoring new evidence or overreacting to it as if nothing else mattered."
Bayesian updating means treating your existing beliefs ('priors') as probabilities rather than fixed facts, then adjusting those probabilities up or down whenever new evidence arrives, in proportion to how strong that evidence actually is — rather than either dismissing the new evidence entirely or discarding your prior knowledge and starting over as if the new data were the only information that mattered.
The mammogram example makes the mechanism concrete: even a mammogram that correctly detects cancer 75% of the time will still produce far more false positives than true positives in absolute numbers if the underlying disease rate is very low (about 1.4% of women under 40) — because a 10% false-positive rate applied to the roughly 98.6% of women who don't have cancer generates a huge number of false alarms that swamps the smaller number of true positives, unless you factor in that low base rate (the prior) before interpreting the test result.
In the mammogram example used in this piece, why can a test that's 75% accurate still produce mostly false positives in absolute numbers?
Read more about the topic
The explanation above is written with AI assistance. These are the originals — go to them to check it.
- Bayes and Deadweight: Using Statistics to Eject the Deadweight From Your LifeFarnam Street
- Julia Galef on Bayesian reasoning changing how you thinkBig Think, via YouTube
The Map is Not the Territory
"Our mental models of reality are reductions. When the model contradicts reality, the model is wrong, not reality."