The medical test paradox, and redesigning Bayes' rule
December 22, 2020
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21:14Now PlayingThe medical test paradox, and redesigning Bayes' rule
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as posted by the channelAbout Likelihood Ratios, also sometimes called Bayes Factors*.
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The book by my friend Matt Cook about paradoxes mentioned at the end:
On the topic, I can't help also mentioning another paradox book I'm rather fond of by Bunch:
Another video on Bayes' theorem:
*As mentioned in the on-screen note at the end, while the terms "Bayes Factor" and "Likelihood Ratio" refer to the same ratio 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:
This post has some nice discussion of the distinction:
Timetable:
Thanks to these viewers for their contributions to translations
French: Raphaël Ventura
Russian: Ilia Konnov
Vietnamese: duyhub
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These animations are largely made using manim, a scrappy open source python library
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.
Music by Vincent Rubinetti.
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