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Re: Bivariate Normal Distributions -- can they be estimated in my lifetime?

• To: mathgroup at smc.vnet.net
• Subject: [mg14824] Re: Bivariate Normal Distributions -- can they be estimated in my lifetime?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 18 Nov 1998 01:29:29 -0500
• Organization: University of Western Australia
• References: <728kgi$egt@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Luci Ellis wrote:

> I have given up on several weeks of work trying to do maximum likelihood
> estimation of a bivariate probit model (ie two binary decisions that
> are correlated). The likelihood function itself is easy to construct,
> and in principle should be easy to maximise (using FindMinimum[] on its
> negative) because the PDF of the bivariate normal distribution is
> single-peaked.
> 
> However, it appears impossible to do this on a desktop computer. 

I have written a short Notebook on a number of ways for computing the
PDF of the bivariate normal distribution.  It is available at

 ftp://ftp.pd.uwa.edu.au/pub/Mathematica/MathGroup/BivariateNormal.nb

> Chris Farr has previously suggested using a discrete approximation of
> the CDF, but I am concerned that the approximation error would get too
> large, making my results unreliable.

Possibly -- but how accurately do you need the PDF?

> Gauss and Stata can both do this -- why can't Mathematica? 

An interesting question: "How accurate are the PDF produced using these
packages?"

> I accept that a general package like Mathematica is going to be slower
> than a specialised package like Stata or Shazam -- but the margin needs
> to be smaller if Mathematica is to be usable in this context.

I think Mathematica certainly _is_ usable in this context!

Cheers,
	Paul

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at physics.uwa.edu.au  AUSTRALIA                       
http://www.physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________

• Follow-Ups:
  • Many data points = frustration
    • From: Brian Boonstra <boonstb@cmg.FCNBD.COM>