The medical test paradox, and redesigning Bayes' rule

Summary by Krater

This video explains the medical test paradox and Bayes' rule, demonstrating how an accurate test can have low predictive value when disease prevalence is low. It contrasts the usual probability formulation of Bayes' rule with an odds-based formulation using Bayes factors to simplify calculations and update probabilities intuitively.

From the video

Answers: Why can an accurate medical test have a low probability of correctness for an individual result?

• Bayes' rule
• Medical test paradox
• Positive predictive value
• Sensitivity and specificity
• Bayes factor and odds

What it concludes

• An accurate medical test can have a surprisingly low positive predictive value when disease prevalence is low.
• Expressing Bayes' rule using odds and Bayes factors makes updating probabilities through multiplication simpler and more intuitive than using traditional probability fractions.
• Test accuracy determines how chances are updated from prior odds, keeping prior probability and test accuracy as separate, clear components.