Date:         Wed, 17 Sep 2008 16:38:12 -0400
Reply-To:     Kevin Viel <citam.sasl@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Kevin Viel <citam.sasl@GMAIL.COM>
Subject:      Re: BBU: computational statistics/numerical analysis

On Wed, 17 Sep 2008 13:27:35 -0400, Peter Flom
<peterflomconsulting@MINDSPRING.COM> wrote:


>I'd be interested, but I don't think that SAS Base is really the ideal
>environment for this
>sort of thing.  I think it would be great to do something like this in
>IML, which would give the reader (e.g. me) an incentive to learn IML as
>well.  With ingenuity, such as you displayed in the code you posted, one
>could probably do a lot, but for what purpose when there are better tools
>(e.g not only IML, but R) available?
>
>There is a well-regarded book doing this, using Mathematica, but the price
of Mathematica is prohibitive for me, and likely for many others.

Peter,

  No doubt that any serious attempt would require IML.  However, some of
the computations could be done using the datastep as a post concerning the
variance of a variable showed last week.  The point would be to make the
calculations, including recursions, plain to the point of pedantic.

  By the way, I coded the recursion I posted based on Kenneth Lange's
explanation in "Numerical Analysis for Statisticians".  By using recursion,
and storing the value of a previous computational, Horner was able to
reduce the number of operations to compute the value of a polynomial of the
nth power from 3n-1 to 2n (n multiplications and n additions).  Beyond
thinking about this computation in terms of efficiency (and understanding
the process in computer science terms), I think being able to perform such
calculations indicates one's mastery-greatly important in the field of
statistics, in which useful things are always a computation (function) of
some (greater) data.  For instance, the sample mean being the summation
divided by n-1....

  Never mind more complex things like a (non-positive definite) Hessian or
the term gradient in NLMIXED... :)

Kind regards,

Kevin