Bayes' rule

I'm working late tonight. There are two things I have to do: Preparing for a meeting next week (boring), and preparing a lecture for tomorrow morning (fun).

The subject I'm gonna teach tomorrow is Bayesian inversion. It's based on the so-called Bayes' rule of mathematical statistics. Bayes' rule is (of course) named after Thomas Bayes (1702-1761) who discovered this relation.

Thomas Bayes was a theologist and mathematician. During his lifetime, he published two articles, one on theology, and one on mathematics. Bayes rule, however, was published after his death. He never got the chance to appreciate the fame it earned him.

Bayes rule is about how a probability distribution is changed if we add some extra information. I'll try to explain. Consider to random variables:

(A): Kids like the dinner and don't complain
(B): We have pizza for dinner

The probability of (A), kids like the dinner is maybe 60% in our family. However, given (B), we have pizza for dinner, the probability is a lot higher. That's easy.

The opposite (or inverse) question is harder. If (A), kids like the dinner, what's the probability of (B), we have pizza for dinner? The kids like other things too, for instance taco and pasta and steak. This question does not have a unique answer.

But if we add the extra information that we have Taco every Friday, pizza every Saturday, and pasta and steak at most once a month, it's a little bit easier. If kids like the dinner, we probably have either pizza or taco. Still we have two equally probable answers (pizza or taco), but the last two (pasta and steak) are less probable.

You see what I mean? Cool, isn't it >:)

(The picture is Bayes rule, where P is the probability and A and B as above. I wrote it down on a sheet of paper and put it on the scanner. Tomorrow I'm gonna write it on the blackboard for the students)

The 3rd worst invention of all time: Pizza with pineapple

Recently, I was going through my blog archive, to delete some old posts that were really bad and not worth keeping. Also, I found that I had forgotten to complete my little trilogy on the "worst inventions of all time".

I had written about the first two
1. Religion,
2. Handguns,
but not the 3rd and last one. So here it is:

The 3rd worst invention of all time: Pizza with pineapple.

I like pizza and I like pineapple, but not at the same time. One of my favorites is pizza with pepperoni, and I really hate it when I get pineapple on top of it, or even worse, when the pineapple is mixed in with the melted cheese.

It's not a big problem, you may say, and I agree. I can order my pepperoni pizza without pineapple, or simply peel them off. Sometimes it's good to have a problem that I can do something about.

I can’t stop all the religious extremism going on, and I can't get rid of all the handguns in the world. But I can at least get the pineapple off my pizza.

Tomorrow the vacation starts; two weeks away from the computer, and with lots of Italian food. Have a nice summer >:)

The worst inventions of all time

This is my top-three list of the worst inventions of all time:
1. Religion (the worst by far; all of them),
2. Handguns,
3. Pizza with pineapple.
I will come back to these items one by one, as soon as I get the time and inspiration to write about the misery.