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ListIntegrate3D ?

• To: mathgroup at smc.vnet.net
• Subject: [mg76697] ListIntegrate3D ?
• From: nottrevorgraham at gmail.com
• Date: Sat, 26 May 2007 04:24:35 -0400 (EDT)

Hi,
I have a list of x,y,z data:
x1, y1, z1
x2, y2, z2
...
xN, yN, zN

That defines a surface z=f(x,y).  I would like to be able to integrate
to compute the area under this surface.

To do this, I assume I need first need to interpolate the surface,
then integrate the interpolated approximation (which will be an
approximation to f(x,y)).  In 2D this seems straightforward, using
NumericalMath`ListIntegrate`.  Could anyone suggest how I could do
this in 3D?

The data is two parameters (x,y) and z is the (log)-likelihood of a
model given the parameters.  I'm trying to integrate the likelihoods
over (x,y) to compute a posterior distribution.

Many thanks for your help.

Trevor