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