3Blue1Brown
4 HN recommenders · recommended in 6 months, 2020–2025
21:14 · 1.4M views · Dec 22, 2020
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.
HN's go-to link whenever Bayesian reasoning, base rates or imperfect tests come up.
7 comments from Hacker News
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] this video
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] this video
3Blue1Brown explains it well. this 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.
Almost no tests in existence can confirm or deny particular infection. Think of them (and symptoms) more as odds updater. If you have 20 minutes to spare this video [0] by 3 Blue 1 Brown is a brilliant introduction to the concept. [0] this video
The advantage of the odds formulation is that you can compute posterior odds in your head, whereas computing the posterior probabilities via the standard form of the theorem (that you wrote down here) involves an unpleasant normalization factor. E.g. for the example in [LINK] : prior odds of infection = 2 : 98 × likelihood ratio = 95 : 5 = posterior odds ≈ 200 : 500 and thus the probabilities (if you actually need them at this point) are ≈ (2/7, 5/7). See also 3Blue1Brown’s exposition: this video .