Bayes theorem, the geometry of changing beliefs

There's a very cool 3Blue1Brown video [0] that helps give you an intuitive feel for Bayes Theorem. [0] [VIDEO]

Wow that's cool. I've always wondered how to do something those swish YouTube videos like 3Blue1Brown[1]. [1] [VIDEO]

This is the classic problem solved by Bayes: [VIDEO] there just aren't that many homeschooled people to provide a defense. I'm another successful homeschooled-until-college adult, but homeschooling isn't that common now and it was even less popular when I was growing up. EDIT: unless you were mentioning defense of homeschooling given they were homeschooled. I would assume most people on HN who were homeschooled had a decent education/homeschooling experience.

> This metric is also a proxy for living in a violent environment. Probably, probably not. The probabilities of witnessing someone being shot is extremely low in both environments. If amount of people who are living in violent environment is much lower, it may be that a person who witnessed someone being shot is more probable from a good environment. [LINK] [VIDEO]

Probably, but more likely a lack of knowledge and an overestimation of their knowledge. People are famously bad with statistics but people are also famously over confident in their understanding of numbers and data. I mean cloud servers really try to get some extra 9s on the end of their uptime. (People are also __terrible__ with rates of change. e.g. 90% increase as from last year). But I think an interesting one is the also literally the most common example that's in many stats textbooks, at least the ones that cover Bayesian stats. That being that if a test is 95% accurate, that it does not mean that that scoring positive on a test means that there's a 95% chance you have whatever the test is testing for. I think there's a great irony in the latter, as I find in the tech and engineering communities a lot of confidence, especially in understanding numbers yet very often make this mistake[0], and frequently want to establish meritocracies (advocating for standardized testing and leet code). But understanding the former should result in thinking the latter is ineffective.[1] -------------------------------- [0] I particularly like 3Blue1Brown's introduction to Bayes theorem as it includes the Kahneman and Tversky questions AND (most importantly) he discusses how when the questions are reframed that peoples accuracy can dramatically swing from overwhelmingly wrong to overwhelmingly correct. I like this because the hardest thing in doing statistics (and much of science) is actu