Visualizing Bayes’ theorem (2009) | Hacker News Reader

Visualizing Bayes’ theorem (2009)

oscarbonilla.com

53 pointsSimplyUseless12 comments

I'm still quite fond of the Lego example:

https://www.countbayesie.com/blog/2015/2/18/bayes-theorem-wi...

The neat thing about the lego example is it uses overlapping grids instead of overlapping circles.

Overlapping circles are familiar -- everyone made venn diagrams in primary school.

Problem is it's notoriously subjective to use circles to map to some quantity. Visualization blogs are rife with examples of people riffing on visualizations that confuse mapping circle radius vs. circle area to some quantity.

Using a grid (or legos) is nice because it eliminates that area-vs-radius ambiguity.

As soon as I've learned bayes theorem myself, I'll go on and teach my 9 year old daughter.

This seems to me to be the best way to understand Bayes' theorem, with natural frequencies being the best way to mentally compute with it. E.g. for the breast cancer example,

- Imagine there are 1000 women who participate in routine screening

- 1% → 10 of these have breast cancer

- 80% → 8 of these will get positive mammograms

- 990 don't have breast cancer

- 9.6% ≅ 10% → 99 of the 990 get positive mammograms

So that the probability of having breast cancer, given a positive mammogram, is ≅ 8/99 ≅ 8%.

There is a bunch of research on natural frequencies being generally the best way to reason about this sort of thing.

I attempted a way to visualize that example (with natural frequencies) here:

https://medium.com/@eshan/why-nobody-understands-mammograms-...

Isn't this the bog standard way to visualize Bayes' theorem?

Still appreciate it though.

Took a entire module on Bayesian Method in University.

Failed it.

Gave the exam a second time - this time I spent the whole summer studying it - failed it again :(

At this point I think bayesian methods is one of those things like Monads - you either understand it or you never will.

Hopefully there is someone out there who finally writes a good book to explain it to the masses of simpler minds.

When I encounter complex subjects like Bayes, I tend to turn to Kalid to see if he has a way of trying to internalize an intuitive understanding of the subject.

http://betterexplained.com/articles/an-intuitive-and-short-e...

Now, this might be too simplified compared to what you were being tested on given you did a whole module on it, but hopefully it helps.

Yeah, Bayes, Monads, and Types: things that every programmer uses "intuitively" but for some reason end up being difficult to grasp when explicitly formalized. At least speaking for myself. You're not alone. Hopefully it will get better for the both of us.

> At this point I think bayesian methods is one of those things like Monads - you either understand it or you never will.

Add organic chemistry to that list. I can write a program from scratch that will accurately simulate how two organic molecules react using density functional theory, but I'll be darned if I ever understand those little diagrams and arrows.

“people with cancer” (designated as A), and “people with no cancer” (or A)

Presumably the second "A" is supposed to appear as some symbol for "not A"? On my screen it just appears to say A.

Bayes Theorem is easy. But determining its components can get tricky.

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