Comments on: What’s Wrong with Probability Notation?

By: Anonymous

Anonymous — Sun, 14 Feb 2010 11:01:02 +0000

This is just standard shorthand probability notation. I.e.,
p(x) is really p(X=x) which is really p_X(X=x), so to do Bayes rule in this complete form we’d get

p_{X|Y}(X=x | Y=y) = p_{Y|X}(Y=y|X=x)p_X(X=x)/p_Y(Y=y)

as in all mathematics,when you use something a lot, you make a shorthand.

By: David Eubanks

David Eubanks — Fri, 30 Oct 2009 01:24:56 +0000

Actually, it’s more complicated than the quote might lead you to believe because x and y are random variables, which each come with their own probability distribution (a function). The p is more like an operator. For example p(x+y) means the distribution you get by adding x and y, which isn’t trivial to compute (it’s a convolution product).

There are easier ways to visualize Bayes’ rule, though. I use tree diagrams when I teach in, and students find it intuitive.

By: Andre Ariew

Andre Ariew — Thu, 22 Oct 2009 15:01:38 +0000

Fortunately there is an easy answer to your question. In a phrase, “natural frequencies”. Gerd Gigerenzer wrote a book about it and how to think about working through Bayesian problems very easily. I teach a large section critical thinking course (based in philosophy) at the University of Missouri and this is one of the things I teach students because after all, every one of them is going to need Bayes to interpret some sort of medical emergency.

Here’s a link to the book: http://www.academicproductivity.com/2009/whats-wrong-with-probability-notation/