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Teaching a short class on Bayes' Theorem?

8 Post author: Tesseract 07 December 2011 09:45PM

At my college, there's a week before Spring Semester each year in which anyone who wants to can teach a class on any subject, and students go to whatever ones they feel like. I'm thinking about teaching a class on Bayes' Theorem. It would be informal, one to two hours long, and focused mostly on non-obvious applications of it (epistemology, the representativeness heuristic, etc.)

At the moment, I'm thinking about how to design the class, so I'd appreciate any suggestions as to what content I should cover, the best format, clear ways to explain it, cool things related to Bayes' Theorem, good links, and so forth.

Comments (15)

Comment author: wallowinmaya 07 December 2011 11:17:47PM 5 points [-]
Comment author: Costanza 08 December 2011 08:53:32PM *  4 points [-]

One true story about Bayes' Theorem that grabbed me when I read it:

My most memorable encounter with the Reverend Bayes came one Friday afternoon in 1989, when my doctor told me by telephone that the chances were 999 out of 1,000 that I'd be dead within a decade. He added, "I'm really sorry," as if he had some patients to whom he would say he is sorry but not mean it.

The author went on to explain that he and his wife had applied for life insurance and had been rejected on the ground that he had apparently tested "positive" for HIV.

I'm reminded that a good portion of the LW community wasn't born in 1989. From what I personally remember about that year, I suggest that this news must have been devastating. For one thing, as I recall, homosexuality was much more heavily stigmatized in general society than it is now. Also, AIDS (in the popular perception) represented a sentence of death by agonizingly slow torture -- I remember hearing about a friend of a colleague who spent months gagging on the growths on his tongue, to name only one of his afflictions. Antiviral treatment was on the way, but nobody knew that in 1989.

The author describes his receipt of this news dryly, but at the time, it must have been as if he had been told: "You're going to die in agony, prolonged over the course of months, if not years. I don't know or care how you got it, but I and everyone else in the world will assume it's because you've been cheating on your wife with homosexual prostitutes. Oh, you should let her know that you've probably infected her, too, dooming her to your horrible disgusting fate. Have a nice day!"

Later on, it turned out to have been a simple mistake -- the test was a false positive, and the 999 out of 1,000 figure had been based on a lack of understanding about Bayes' Theorem.

Comment author: shminux 07 December 2011 11:47:37PM *  9 points [-]

If you want people to sign up for your class, don't call it Bayes Theorem, or anything equally boring (not many people can even pronounce "representativeness heuristic" on the first try).

Maybe something along the lines of "One fraction to rule them all" or "When a 99% positive test is only accurate 1% of the time" or something similarly catchy.

Comment author: J_Taylor 08 December 2011 06:29:32AM 3 points [-]

Something about posteriors?

Comment author: Dan_Moore 08 December 2011 02:23:54PM 0 points [-]

If you want people to sign up for your class, don't call it Bayes Theorem, or anything equally boring (not many people can even pronounce "representativeness heuristic" on the first try).

Maybe something along the lines of "One fraction to rule them all" or "When a 99% positive test is only accurate 1% of the time" or something similarly catchy.

I think 'Bayes' Theorem' (but perhaps not Bayes's Theorem) is catchier than the latter two suggestions. Also clearer.

Comment author: cata 07 December 2011 10:25:30PM *  3 points [-]

It would be cool if you found a way to work in the existence of Cox's theorem -- when I encountered it, I had never thought about why the laws of probability were given as they are, or if there could be a different consistent way to represent and calculate probability besides multiplying numbers together. So it made a big impression on me.

I don't know how to make that part of a more layman-oriented discussion of probability and epistemology, though.

Comment author: buybuydandavis 08 December 2011 07:39:02AM 1 point [-]

That's a big point for me too. Show that it solves a problem, instead of being a formalism you just happen to use for reasoning under uncertainty for some unknown reason.

Comment author: Axel 08 December 2011 12:32:18PM *  2 points [-]

I'm studying to be a teacher so I'll try and give you some of the theory we get.

First things first: keep in mind who your audience is, this determines what type of lesson is most effective. What age group are they in? What is their foreknowledge of Bayes' Theorem? Do they have any special interests you could use in your class? What subjects are they studying at your college?

If you only get to teach one class on the subject I suggest going easy on the amount of content. You will never be able to fit all of the applications of Bayes Theorem in one hour so pick one or two and make it look awesome. Getting students hooked is the hard part but once you do they'll start learning on their own.

Most people don't like things that are to abstract and long formula's tend to scare them off. Be very specific and use a lot of real world examples. Shokwave made an excellent suggestion here: an overarching theme to serve as a guiding principle. Betting is a good idea but try and give it a very specific setting: horse races, betting on the elections, card games, betting on a sports event (if your college has a sports team you can use them) Let them actually do stuff, don't just give an hour long lecture.

Last but not least: be enthusiastic about the subject! If they see you having fun with it, chances are they'll have a good time as well.

If you can give me some more background information on the students and what content you wish to cover I could throw some ideas your way.

Comment author: Grognor 08 December 2011 08:48:57AM 2 points [-]

XiXiDu has an excellent collection of almost all the good stuff on the internet about Bayes' Theorem here. I actually found some of these really helpful when I was going through them, especially the visual guides.

So, my contribution to this thread is to say you should use those visual guides.

Comment author: XiXiDu 08 December 2011 12:03:03PM 0 points [-]

There is more here. I have to update both pages.

Comment author: Goobahman 08 December 2011 01:48:58AM 2 points [-]

If you send me your email I can send you a copy of a powerpoint I made a while back when I was running a short talk on Bayes Theorem.

most of it I got from here however:

http://commonsenseatheism.com/?p=13156

<3 lukeprog

Comment author: Kaj_Sotala 10 December 2011 10:53:49AM 1 point [-]

I think you shouldn't use the doctor example nor any math toy problem example at first. Instead, discuss some easy-to-understand examples from everyday situations first, and only then present the math behind it. Then discuss some mathy problems. Then go back to more everyday situations.

At least for people who aren't afraid of math, understanding the math is relatively straightforward: understanding how it applies to their lives is the tricky part.

Comment author: Teal_Thanatos 08 December 2011 06:15:33AM 1 point [-]

Hi, I Sincerely hope you will also put this on youtube....

Comment author: shokwave 08 December 2011 01:46:38AM 1 point [-]

To make it catchy, you could use the theme of betting. Introduce the concept of acting on beliefs as taking a bet (except you get paid in job offers instead of poker chips and so on) and work from there.

Comment author: buybuydandavis 08 December 2011 07:39:26AM *  0 points [-]

Show them the problem a few days back with the coins and envelopes. That was the best problem to demonstrate the difference between probability as propensity and probability as reasoning based on information that I've ever seen.