About Likelihood Ratios, also sometimes called Bayes Factors*. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/bayes-factor-thanks Home page: https://www.3blue1brown.com/ 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://www.youtube.com/watch?v=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 Thanks to these viewers for their contributions to translations French: Raphaël Ventura Russian: Ilia Konnov Vietnamese: duyhub ------------------ 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. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com/ Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown