For low dimensions (2-3), I think it's relatively efficient to use
standard quadrature techniques with the multivariate normal pdf. For
higher dimensions (e.g., required by some multivariate probit
models), economists like to use GHK (Geweke/Hajivassiliou/Keane). I
know you can use this algorithm to efficiently simulate definite
integrals (constant bounds) of multivariate normals and I'm pretty
sure it can handle +/-inf bounds too. Technically, the algorithm
lets you sample from bounded multivariate normals which you then use
to compute probabilities. It's not implemented in GSL, but the
algorithm isn't terribly complicated. It was developed
independently in Geweke (Computing Science and Statistics:
Proceedigns of the Twenty-third Symposium on the Interface,
"Efficient Simulation from the Multivariate Normal and Student-t
Distributions Subject to Linear Constraints", 1991) and
Hajivassiliou, McFadden, and Ruud (Yale Working Paper, "Simulation of
Multivariate Normal Orthant Probabilities: Methods and Programs",
1991). I'm sure there's a more recent more easy to find reference
too. In fact, Hajivassiliou and Ruud's chapter in vol 4 of the
Handbook of Econometrics (1993) has a succinct description of the
method.
Doug
---------------
Doug McKee
Post-doctoral Scholar
University of Pennsylvania
Population Studies Center
[EMAIL PROTECTED]
310-266-2438
On Sep 27, 2007, at 4:43 PM, [EMAIL PROTECTED] wrote:
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Message: 1
Date: Mon, 24 Sep 2007 10:03:17 +0200 (CEST)
From: [EMAIL PROTECTED]
Subject: Re: [Help-gsl] Question
To: [email protected]
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At Thu, 20 Sep 2007 11:32:06 +0200 (CEST),
[EMAIL PROTECTED] wrote:
Currently, I am working with GSL library and in fact I am looking
for a
function that returns the upper tail (lower tail) associated with a
multivariate Normal distribution. I would like to know if for the
next
version of GSL, you have planned to develop this function or if
it could
be possible to develop it. Thanks for your informations.
Hello,
What is the definition of an upper tail in more than one dimension?
--
Brian Gough
(GSL Maintainer)
Network Theory Ltd,
Publishing the GSL Manual - http://www.network-theory.co.uk/gsl/
manual/
Hello,
I give you the definition of a lower tail associated with a
multivariate
Normal distribution in the enclosed file.
If you need further informations, don't hesitate to contact me.
Regards.
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