# Why Bayes rule is nicer with odds

From 3Blue1Brown.

About Likelihood Ratios, also sometimes called Bayes Factors*.
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The book by my friend Matt Cook about paradoxes mentioned at the 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

Another video on Bayes’ theorem:
https://youtu.be/HZGCoVF3YvM

*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:
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

Timetable:
0:00 – What is the paradox?
5:53 – The Bayes factor
11:00 – The snazzy Bayes rule
14:42 – Contrast with the usual formula

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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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https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

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