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The medical test paradox, and redesigning Bayes' rule

3Blue1Brown · 1.4M views · 2020-12-22 · 21:14

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Overview

3Blue1Brown explains why positive results on accurate medical tests are often false positives, and reframes Bayes' rule using likelihood ratios (Bayes factors) to update odds. It uses visual examples to make the reasoning intuitive.

On Hacker News

HN's go-to link whenever Bayesian reasoning, base rates or imperfect tests come up.

Recommended by 4 HN people across 4 months · HN mentions 2020–2025

Topics

Probability & game theoryRecreational & visual math
Search by tags
bayes factorlikelihood ratiobase ratemedical testsprobability

What people said

drewmate · 2020-12 · Strong recommendation

I agree that this is definitely a trend, so I feel like highlighting a great example of educational content that is very dense, concise, and with just a touch of whimsy: 3Blue1Brown on Youtube[0]. He has been doing math education videos on YouTube for years. I just watched his latest video on the medical test paradox and redesigning the Bayes rule to address it[1]. All his videos are absolutely phenomenal - the best educational content I've seen on YouTube. I cannot recommend them highly enough. In my experience it is more akin to reading a (very engaging) textbook than watching a video. I often find myself pausing to think things through and can _feel_ myself grasping at new ideas and learning while watching. [0] [LINK] [1] [VIDEO]

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V__ · 2025-08 · Recommendation

I really like this video [1] from 3blue1brown, where he proposes to think about significance as a way to update the probability. One positive test (or in this analog a study) updates the probability by X % and thus you nearly always need more tests (or studies) for a 'meaningful' judgment. [1] [VIDEO]

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andersrs · 2024-01 · Recommendation

3Blue1Brown explains it well. [VIDEO] If the population who do _not_ actually have serious cancer is orders of magnitudes larger than those who do then there will be far more people in the false positive group than the true positive group and thus the vast majority of operations will be unnecessary.

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Sources

Video by 3Blue1Brown, played through YouTube.

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