Probability & Calibration
Base rates · Updating · Humility
The chance something is “true given evidence” is not the chance you see the evidence if it is true.
— Phyllux Media
Confusing P(A|B) with P(B|A) ruins doctors’ mornings and pundits’ evenings. This essay rehearses base rates, likelihood, and why slow thinking still outsources to spreadsheets when stakes climb.
I. Start With the Base Rate
Rare things stay rare even with “accurate” tests
If a condition affects one in a thousand people, even a highly specific test can generate more false positives than true positives when infection is rare. Arithmetic, not temperament.
Teaching trick: always sketch the population before you stare at the flashy sensitivity number.
II. Update, Do Not Teleport
Bayes as disciplined belief revision
Posteriors combine priors and likelihoods. New evidence shifts mass; it rarely vaults you from “impossible” to “certain” without extreme likelihood ratios.
If someone reports a Bayes factor, ask what went into the prior space.
III. Calibration as Character
When your 70% hits should land 70% of the time
Calibration measures whether your stated confidences match frequencies over many trials. Experts can be sharp but miscalibrated; training helps.
Forecasting tournaments reward people who know what they do not know.
IV. Headlines Pump Likelihood
Why “study proves” triggers misfires
Science news often reports P(data|hypothesis) vibes while readers hear P(hypothesis|data). Demand effect sizes, sample design, and preregistration when stakes matter.
Phyllux media essays are not peer review—go to primary literature for claims that need it.
Slow Down, Multiply
Probability is grammar for uncertainty. Learn the grammar once; use it for life.
Carry a base rate in your pocket.