Posterior

My Journey From Frequentist to Bayesian Statistics

Type I error for smoke detector: probability of alarm given no fire=0.05 Bayesian: probability of fire given current air data Frequentist smoke alarm designed as most research is done: Set the alarm trigger so as to have a 0.8 chance of detecting an inferno Advantage of actionable evidence quantification: Set the alarm to trigger when the posterior probability of a fire exceeds 0.02 while at home and at 0.

Clinicians' Misunderstanding of Probabilities Makes Them Like Backwards Probabilities Such As Sensitivity, Specificity, and Type I Error

Imagine watching a baseball game, seeing the batter get a hit, and hearing the announcer say “The chance that the batter is left handed is now 0.2!” No one would care. Baseball fans are interested in the chance that a batter will get a hit conditional on his being right handed (handedness being already known to the fan), the handedness of the pitcher, etc. Unless one is an archaeologist or medical examiner, the interest is in forward probabilities conditional on current and past states.