Re: A stats library (announcement)
- From: "Reef Fish" <Large_Nassau_Grouper@xxxxxxxxx>
- Date: 5 Jul 2005 11:32:03 -0700
Reef Fish wrote:
> Anon. wrote:
> > Reef Fish wrote:
> > >
> > <snip>
> > >
> > > No problem with SPEAKEASY.
> > >
> > > http://www.speakeasy.com/about_speakeasy.htm
> > >
> > > < excerpted from my previous post>
> > >
> > > It was developed in the 1960s, by a physicist Stan Cohen while he
> > > was at a National Lab in physics. It is, by far, and to date, the
> > > MOST POWERFUL and MOST VERSATILE language, for mathematics,
> > > statistics, physics, and many other related areas., cncompassing
> > > these mathematical techniques:
> > >
> > > logical, conditional, and relational evaluations
> > > numerical integration and differentiation
> > > differential equation solutions
> > > linear and quadratic programming
> > > fast Fourier transformations
> > > statistical analyses
> > > optimization routines
> > > and many others!
> > >
> > What statistical analyses is it capable of?
>
> Because it is not a statistical package, but a powerful language, it
> is capable of doing nearly ALL of the statistical methods in
> univariate and multivariate analysis and monte carlo methods
> in graduate courses I've taught in those subjects, as well as many
> of the statistical methods in journal papers I've read or refereed
> that are NOT found in ANY package, because it's so easy to program
> something difficult or cumbersome to do in other languages.
>
> For example when I was teaching model building, I wrote most of
> the routines, including one in all possible subsets, with EVERYTHING
> in diagnostics (Mallow's CP, Hocking's Jp, etc.) in the Cook and
> Weisberg textbook, including tabulations, plots, etc., in a TOTAL
> of less than 10 LINES of the basic language!
Now I remembered that I actually used a crude version (1980s) of that
program to illustrate the use of SPEAKEASY for statistical computations
of what's in Cook and Weisbert's book when I gave an invited talk at
the U of Minnesota, where Cook and Weisberg were in the audience. :-)
The Hamiltonian sequence to generate ALL possible subsets of k
variables in the most efficient was of doing 1 SWEEP at a time
is given by
1 (2) 1 (3) 1 2 1 (4) 1 2 1 3 1 2 1 (5) ...etc.
where each index brings a variable IN if it's not in the equation,
and takes it out if it is, will generate ALL combinations in this
order (note its NOT the lexicographical order which is VERY
inefficient):
x1; x1 x2; x2; x2 x3; x1 x2 x3; x1 x3; x3; x4; ...
where each combination appears ONCE, and only ONCE, requiring
a fraction of the work to invert the X'X matrix by only sweeping
over exactly ONE pivotal element of the X'X matrix!
DO loops are RARELY needed in the language, but this is the
entire CODE that generates the entire hamiltonian sequence of
length 2^K, the code below suffices:
HAM=1; FOR I=2,K; HAM = HAM,I, HAM; NEXT I
The few examples I've shown should give one a sense of the POWER
of the basic language.
-- Bob.
>
>
> The statistical analyses that are built in the "Statistical Analyses"
> are not very good, but adequate for many elementary or routine
> analyses. The WORDS (functions) include the calculation of binomial,
> gaussian, chi-square, t, and F probabilities and inverse probs,
> some times series functions, regression analysis functions, and
> nonparametric tests such as the Kolmogorov-Smirnov one sample test.
>
> BUt the LANGUAGE itself is so powerful, one hardly need ANY built-in
> procedures, but can write ONE-LINE programs or subroutines or
> FUNCTIONS to compute special tasks, or insert conversational requests
> for I/O rather than having to remember the necessary arguments of
> a program of subroutine.
>
> For example, if all you want are the LS regression estimates for
> a UNIVERIATE or MULTIVARIATE regression, this ONE LINE will suffice:
>
> b = inverse(transp(X)*X)*transp(X)*Y
>
> where "inverse" and "transp" are basic SPEAKEASY functions.
> Also, the reciprocal of a matrix is understood to mean "inverse", so
>
> b = 1/(transp(X)*X)*transp(X)*Y
>
> will accomplish the same.
>
> If Y is a vector, b is the univariate LS estimated b.
> If Y is a matrix of more than one Y, b multivariate regr estimated B.
>
> -- Bob.
.
- References:
- Re: A stats library (announcement)
- From: David A. Heiser
- Re: A stats library (announcement)
- From: Mr. BK of Baltimore, MD
- Re: A stats library (announcement)
- From: beliavsky
- Re: A stats library (announcement)
- From: Evgenii Rudnyi
- Re: A stats library (announcement)
- From: Reef Fish
- Re: A stats library (announcement)
- From: Anon.
- Re: A stats library (announcement)
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