Bayes' Theorem Illustrated

http://lesswrong.com/lw/2b0/bayes_theorem_illustrated_my_way/

by astrofinch • 14 years ago

160 13 14 years ago

lovely explanation , very clear!

taliesinb• 14 years ago

Bayes' 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/

ovi256• 14 years ago

The 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• 14 years ago

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.

SoftwareMaven2• 14 years ago

This 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• 14 years ago

From the same author, http://oscarbonilla.com/2009/05/the-monty-hall-problem/

shriphani• 14 years ago

Being 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• 14 years ago

I don't quite get the steps after cutting off the other branches. The original diagram didn't seem to get updated.

SoftwareMaven2• 14 years ago

The 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• 14 years ago

There should be a law that you only get one paragraph and one figure when explaining Bayes' rule.

dlss• 14 years ago

This

andrewcamel• 14 years ago

I'll give it a shot and get back to you. Should be doable.

thebooktocome• 14 years ago

Why?

Bayes' Theorem Illustrated

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