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)
CaH, I find it really interesting that he had 2 articles published during his lifetime, and this important one after his death. Nowadays we expect our academics to continually publish papers - I wonder how many of them become important enough that people in the future will become excited by them.
ReplyDeleteYou've explained it so clearly I think I understand. Hope your students enjoy the class.
Maths and theology? Interesting combination. After that you lost me, I'm afraid, although that was probably because (being on another diet) all that talk of pizza and tacos distracted me! (I must just wipe the drool off my screen) :)
ReplyDeleteJudy (South Africa)
You do well at putting all this into plain language. I've learned a little about Bayes, but this may be the first time I remember it.
ReplyDeleteI don't have a head for math, but I've always been fascinated by logic and probability. Hope the lecture went well!
ReplyDeleteLooking forward to your answers in the Bernard Pivot Blogfest!
sue: The race for publications is a desease of research. They're counted by the number, and not by quality. The good and interesting articles are drowned in a flood of repitition and minor alterations of well known results.
ReplyDeleteJudy: Yes, theology and statistics is an interesting mix. I doesnt happen often anymore that part-time scientists give important contributions to research.
Hart: Thanks. Bayes rule is easy to use, and also easy to misuse. The statistics community is split into a Bayesian fraction and a frequentist fraction. They're like Cahtolics and Protestants >:)
Nicole: Thanks for visiting. Yes, the lecture went well, continuing this week >:)
I wish my Phyisc teacher sounded this simple. I could have continue and become Einstein by now, perhaps.
ReplyDeleteI had to learn this a few times and I always forget it later. Glad to know there are people like you who can teach me over and over again....
ReplyDelete:)
Thanks for such a simple explanation of a complex subject. :)
ReplyDeleteWe had pizza for supper tonight...
Enid: Good teachers are imprortant. I had an excellent math and physics teacher in high school.
ReplyDeleteLydia: I'm happy if I can teach you once again. I like teaching very much >:)
Elizabeth: My pleasure. I hope you enjoyed your pizza, with or without Bayes in mind >:)
Fascinating details about Bayes, and I enjoyed your examples--very relatable.
ReplyDeleteAll I know is that I am hungry now. I'll take pizza, tacos or pasta.
ReplyDeleteI should get my daughter to read this. She's a math whiz in my book - and she didn't get it from me. But she didn't get either of her degrees in Mathematics.
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