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[Help-gsl] Re: Help-gsl Digest, Vol 47, Issue 20

From: Doug McKee
Subject: [Help-gsl] Re: Help-gsl Digest, Vol 47, Issue 20
Date: Thu, 27 Sep 2007 23:15:37 -0400

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 McKee
Post-doctoral Scholar
University of Pennsylvania
Population Studies Center

On Sep 27, 2007, at 4:43 PM, address@hidden wrote:

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Message: 1
Date: Mon, 24 Sep 2007 10:03:17 +0200 (CEST)
From: address@hidden
Subject: Re: [Help-gsl] Question
To: address@hidden
Content-Type: text/plain; charset="iso-8859-1"

At Thu, 20 Sep 2007 11:32:06 +0200 (CEST),
address@hidden 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.


What is the definition of an upper tail in more than one dimension?

Brian Gough
(GSL Maintainer)

Network Theory Ltd,
Publishing the GSL Manual - manual/


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.


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