4 ms·
Bayes' Theorem Illustrated
- drstrangevibes 15y agolovely explanation , very clear!
- taliesinb 15y agoBayes' rule is quite easy to understand as a Venn diagram, though the linked article doesn't seem to use this fact. But here's a blog-post that does: http://oscarbonilla.com/2009/05/visualizing-bayes-theorem/ http://oscarbonilla.com/2009/05/visualizing-bayes-theorem/
- ovi256 15y agoThe Venn diagram makes visualizing the update so easy, you start to wonder why the Bayes rule is a "thing" at all. It works especially well with the examples, like Yudkowsy's breast cancer screeening example.
- dmfdmf 15y agohttp://www-biba.inrialpes.fr/Jaynes/cc02m.pdf http://www-biba.inrialpes.fr/Jaynes/cc02m.pdf Jaynes argues here (pg 221) that examples were Venn diagrams apply are special cases. According to Jaynes, Bayes theorem is more general than that.
- SoftwareMaven 15y agoThis works well for the cancer example. I'm not picturing how it would work for the Monty Hall problem. Guess it's time to open the drawing app.
- jbellis 15y agoFrom the same author, http://oscarbonilla.com/2009/05/the-monty-hall-problem/ http://oscarbonilla.com/2009/05/the-monty-hall-problem/
- shriphani 15y agoBeing able to prove the Total Prob. Theorem and from there the Bayes Theorem has helped me solve problems (granted from a textbook and not real-life ones). -> In the problem, the sample space comes divided into mutually disjoint portions. -> Using the definition of probability, we can compute joint distribution from the a-priori distributions. -> Using the definition of conditional probability, we can flip around the inference direction. I usually find that all problems (Naive-Bayes spam, cancer) etc. all show this pattern.
- Tycho 15y agoI don't quite get the steps after cutting off the other branches. The original diagram didn't seem to get updated.
- SoftwareMaven 15y agoThe original diagram isn't important any more. It is replaced by the new values that are the results of the experiment. Kind of like: world = get_world() for experiment in experiments(): world = combine(world, experiment()) The original world doesn't exist after the first experiment. The experiment has provided us a new world.
- equark 15y agoThere should be a law that you only get one paragraph and one figure when explaining Bayes' rule.
- dlss 15y agoThis
- andrewcamel 15y agoI'll give it a shot and get back to you. Should be doable.
- thebooktocome 15y agoWhy?