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

[Doug McKee]

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
address@hidden
310-266-2438


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

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> Date: Mon, 24 Sep 2007 10:03:17 +0200 (CEST)
> From: address@hidden
> Subject: Re: [Help-gsl] Question
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> > 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.
> >
> > 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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