On Sun, 21 Jun 2009 02:23:11 +0000, Martin Eisenberg wrote:

> Tim Wescott wrote:
>
>> Yup. Given a PDF I'd _like_ to be able to solve for the expected value
>> of the four vector elements, as well as their cross-correlation. I'd
>> like this to be in a form that's tractable enough that I can code it
>> into an algorithm without either making people's heads explode when
>> they read it and without making the processor bog down.
>>
>> But for now I'll just settle with being able to get the element means
>> and variances out of the thing for a variety of variances of the
>> Gaussians, or a clear indication that if I insist on using Gaussians
>> the math is going to be hopelessly intractable.
>
> How have you decided to project the Gaussian from Euclidean space to the
> 3-sphere?
>
>
> Martin

You mean from Euclidean 3-space to the surface of the 4-sphere? I'm
still trying to figure that out!

I'm finding this an interesting challenge -- I'm not nearly as strong in
this sort of mathematics as I am with visualization. Unfortunately, I
have yet to succeed at visualizing four dimensions (silly me). So I'm
getting better at the math as fast as I can.

--
http://www.wescottdesign.com