The medical test paradox: Can redesigning Bayes rule help?

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From 3Blue1Brown.

Bayes factors, aka Likelihood Ratios*, offer a very clear view of how medical test probabilities work.
Home page: https://www.3blue1brown.com
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The book by my friend Matt Cook about paradoxes mentioned at then end:
https://amzn.to/3aBrEzg

On the topic, I can’t help also mentioning another paradox book I’m rather fond of by Bunch:
https://amzn.to/3mBDSKE

*As mentioned in the on-screen note at the end, while the terms "Bayes Factor" and "Likelihood Ratio" refer to the same term in this setting, where Bayes rule is used on the probability of an event with only two possible outcomes (you either have the disease or you don’t), they do take on divergent meanings in more general contexts. Namely, if you have a continuous parameter you are trying to estimate, the two terms reflect two alternate approaches you can use in comparing hypotheses. In fact, some people take the phrase "Bayes factor" to _specifically_ refer to its use in this more continuous context.

If you want more details, Wikipedia actually has a really nice example discussing the difference:
https://en.wikipedia.org/wiki/Bayes_factor#Example

This post has some nice discussion of the distinction:
https://stats.stackexchange.com/questions/27345/likelihood-ratio-vs-bayes-factor

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These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it’s not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

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