Posted by Michael Neale on November 06, 1997 at 15:36:03:
In Reply to: integration of n-D gauss. dist for finite limits posted by mike osborn on October 10, 1997 at 14:22:09:
I'm looking for a wrapper that would do the same thing.
It is not generally 2**n calls that are required,
because at the edges one saves an n. Better still
it is possible to reduce the dimensionality and thus
'peel' the likelihood. I'm considering writing such
a wrapper unless there is one out there. Anybody?
There is also multivariate normal integration from
the routines of Genz, and from Schervish. These
have been patched into Mx (http://views.vcu.edu/mx)
which can be used to compute the integrals you require
via the \mnor or \muln functions. Genz (\mnor) is
usually much faster but does seem to get stuck at times.
: I'm loking for an efficient FORTRAN routine to
: integrate the volume under a multi-dimensional
: gaussian surface with arbitrary covariance
: over definite (sometimes small) limits. I've
: found the algorithm referenced below, but it does the
: job from -infinity to a set of limits. For an n-D
: calculation I think I have to do 2**n calls to this
: routine to get the right answer (for example: to
: integrate from X1 to X2 and Y1 to Y2, you have to call
: DMV for X2,Y2 + X1,Y1 - X1Y2 - X2Y1).
: Any suggestions?
: C ALGORITHM 725, COLLECTED ALGORITHMS FROM ACM.
: C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
: C VOL. 19, NO. 4, DECEMBER, 1993, P. 546.
: IMPLICIT DOUBLE PRECISION (A-H,O-Z)
: C DMV CALCULATES THE MULTIVARIATE NORMAL INTEGRAL.
: C THE INTEGRAL LOWER LIMITS ARE -INFINITY FOR ALL VARIABLES.
: C THE UPPER LIMITS ARE GIVEN BY THE VECTOR H (INPUT).
: C THE CORRELATION MATRIX IS R (INPUT).