Today, I present to you Bayes theorem like you have never seen it before.

Take a moment to think: how would you calculate a Bayesian update using only basic geometry? I.e., you are given (as line segments) a prior P(H), and also P(E | H) and P(E | ~H) (or their ratio). How do you get P(H | E) only by drawing straight lines on paper?

Can you think of a way that would be possible to implement using a simple mechanical instrument?

It just so happens that today I noticed a very neat way to do this.

Have fun with this GeoGebra worksheet.

And here's a static image version if the live demo doesn't work for you:

Your math homework is to find a proof that this is indeed correct.

Hint: Vg'f cbffvoyr gb qb guvf ryrtnagyl naq jvgubhg nal pnyphyngvbaf, whfg ol ybbxvat ng engvbf bs nernf bs inevbhf gevnatyrf.

Please post answers in rot13, so that you don't spoil the fun for others who want to try.

Edit: For reference, here's a pictograph version of the diagram that came up later as a follow-up to this comment.

Suppose you want to assign a probability that a government will fall (ie the Prime Minister resigns) before the end of the year. Lacking any particular information - I haven't even told you which government it is - you say "Obviously, it's 50% - either it happens or not" (or perhaps "Oh, say, 10%, governments can usually rely on lasting a year at least"), put that prediction into your registry, and go on with your life. Then, on December 1st, you hear that the Prime Minister in question has promised to resign and call an election in March of next year. How should this affect your probability that he will resign before the end of this year?

I see several arguments:

1. Having gotten this public commitment out of him, his opponents have no particular reason to push his government further. It should become more stable for the finite time it has left. My probability of a resignation in December should go down.

2. His opponents were able to extract such a promise; it follows that he cannot be quite confident in his ability to survive a vote of no confidence. Such a signal of weakness might easily lead to a "blood-in-the-water" effect whereby his opponents become more aggressive and go for the immediate kill. His government will surely fall before this attempted compromise date; my probability should go up.

3. The March date wasn't chosen at random. Presumably there is something the PM thinks he can get accomplished if he retains his position until March, but not if he resigns right away. So, presumably, his opponents will be all the more eager for him to resign before he gets it done, whatever it is; they will put more resources into toppling him. Again, my probability should go up.

The question is not hypothetical: I was faced with precisely this problem in December, and got it wrong. I'd like to see how others think about it.

Potentially of interest to my fellow antipodean LessWrongers. Stasis Systems Australia is a company seeking to start a cryonics facility in Australia. Their website is pretty sparse, but they just sent out a mailing list update on how they are going, and it doesn't appear that the information therein is located in any news section of the website, so I thought I'd post it here.

Hello,

We at  Stasis Systems Australia Ltd are happy to report our plans to build a cryonics facility in Australia are progressing well.

You may remember contacting us or attending our online meeting last year, but here's a quick reminder of what we're doing.

We are a group of Australasian cryonicists putting together a non-for-profit organisation to build and run the first cryonic storage facility in the southern hemisphere.

We're proud to have WA-based Marta Sandberg on the board of directors as an advisor, as she has a wealth of knowledge and experience from her ongoing role as a director of the  well-established Cryonics Institute.

We are now officially incorporated as a not-for-profit company, and one investor away from the magic number of ten that will trigger the next stage of the project - selecting a piece of land and starting construction!

We have had productive discussions with the NSW Department of Health, and are developing positive relationships with the Cryonics Institute, Alcor, and KrioRus.

We think what we’re doing is worthwhile and in the long term will be of great benefit to the Australasian community.  If you’d like to get involved either as an investor or a volunteer, that would be fantastic.  We’d love help with articles for the website, search engine optimisation, web graphics, or any other skill you have that we might need.

We would especially appreciate you passing this update on to anyone you know who might be interested.

 

Best regards,

The Stasis Systems Australia team

www.StasisSystemsAustralia.com

 

Follow @StaSysAus on Twitter

Like StaSysAus on Facebook

An easy way to win cheep karma on LW:

1. Publicly make a mistake.
2. Wait for people to call you on it.
3. Publicly retract your errors and promise to improve.