🚀 go-pugleaf

In article <1992Nov2.135009.29552@abo.fi> SASPLUND@finabo.abo.fi (Staffan Asplund AT) writes:
>A question about which critera to use when doing experimental planning.
>A group of people here at my laboratory is talking in favor of using
>a critera of the following kind:
>   maximum ( determinant( transpose(X) * X ) ) 
>
	The D-optimality criterion is based on the product of the
eigenvalues of (X'X)**(-1) and is small when only one of these
eigenvalues are small.
	A new criterion is based on the mean standard error of a random
test of u'b; that is the expectation over the unit sphere of a random
linear inference.  This is equivalent to looking at the (1-alpha)
confidence region for the b's and computing the mean shadow of the
ellipsoid in a random direction.  The problem of computing the mean
radius of an ellipsoid is numerically equivalent to computing the
surface area of an ellipsoid, which had been a long-standing problem for
p>=4.  This problem has been recently solved by Charles Dunkl and Don
Ramirez of the University of Virginia and will appear in The
Transactions of Mathematical Software ACM.   Their code produces the
surface measure of an ellipsoid and the mean radius which is equivalent
to the new criterion for choosing optimal designs given above.
	The code is in Fortran and is available from der@virginia.edu.

--
* Don Ramirez        * Dept. of Mathematics          *  I would  *
* der@virginia.edu   * University of Virginia        *   rather  *
* (804) 924-4943     * Math-Astronomy Building       *   be in   *
* (804) 982-3084:fax * Charlottesville, VA 22903 USA *  Antigua  *