This video I’ve been meaning to watch for a while now. It another great visual explanation of a statistics topic by the 3Blue1Brown Youtube channel (which I’ve covered before, multiple times).
This time, it’s all about Bayes theorem, and I just love how Grant Sanderson explains the concept so visually. He argues that rather then memorizing the theorem, we’d rather learn how to draw out the context. Have a look at the video, or read my summary below:
Grant Sanderson explains the concept very visually following an example outlined in Daniel Kahneman’s and Amos Tversky’s book Thinking Fast, Thinking Slow:
Steve is very shy and withdrawn, invariably helpful but with very little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.”
Is Steve more likely to be a librarian or a farmer?Question from Thinking Fast, Thinking Slow
What was your first guess?
Kahneman and Tversky argue that people take into account Steve’s disposition and therefore lean towards librarians.
However, few people take into account that librarians are quite scarce in our society, which is rich with farmers. For every librarian, there are 20+ farmers. Hence, despite the disposition, Steve is probably more like to be a farmer.
Rather than remembering the upper theorem, Grant argues that it’s often easier to just draw out the rectangle of probabilities below.
Try it out for yourself using another example by Kahneman and Tversky: