# Re: integration of n-D gauss. dist for finite limits

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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.

Mike Neale

: 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?

: reference:
: 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
: C
: C DMV CALCULATES THE MULTIVARIATE NORMAL INTEGRAL.
: C
: 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).