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Re: covariation and declarative randomness RE: Re (2): Turing completeness and syntactic elegance;

From: Steve Schafer <steve@fenestra.com>
Date: Tue, 04 Dec 2012 13:27:23 -0500
To: "David Dailey" <ddailey@zoominternet.net>
Cc: <www-svg@w3.org>, "'Eric Elder'" <ericjelder@gmail.com>
Message-ID: <6kdsb8p6fs822faess9asmsa60ib3nj5tb@4ax.com>
On Tue, 4 Dec 2012 07:29:10 -0500, you wrote:

>What we'd like to be able to add in, and welcome suggestions for how to
>do it, is to be able to control the amount of covariation between two
>random variables --- for example as the y position of trees varies we
>might also want their brightness to increase (but with a fixed
>coefficient of correlation). It is the co-dependency of random
>variables for which we are trying to craft a declarative solution.

Can you give some concrete examples? I'm not sure I understand what
kinds of covariance you're looking for. There is quite a bit of
literature covering joint probability distributions of random variables,
with all manner of combinations of correlation and independence.

I'm reasonably confident that any useful joint probability distribution
can be specified in terms of functions of a finite number of
independent, uniformly-distributed random variables. That is, given a
set A, B, C, etc. of variables of interest (that may be involved in
various degrees of correlation and dependence), and a set a, b, c, etc.
of independent random variables, you should be able to write:

 A = f1(a, b, c, ...)
 B = f2(a, b, c, ...)
 C = f3(a, b, c, ...)
 ... 

If you do it right, then some of the parameters in the functions f1, f2,
etc. could serve as the "knobs" that a non-technical user would be able
to tweak to vary the effect. How you would go about that is left as an
exercise for the reader. ;-)

-Steve Schafer
Received on Tuesday, 4 December 2012 18:27:41 GMT

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