[R] Covariance matrix for GMM

[Ben Bolker]

  I think the problem (for me at least) is that you haven't stated the
problem quite clearly enough.  I may (quite probably) be missing
something; the means clearly combine additively (mean=a1*u1+a2*u2), I 
think the covariances combine additively as well.

  In addition, you may not be getting much in the way of answers because 
this is a general stats/probability question, not an R question.  People 
on this list sometimes answer general questions if they're feeling 
particularly generous and/or interested, but it's not the general purpose 
of the list; you could try the newsgroup sci.stat.consult ... 

  Ben Bolker


On Tue, 11 Feb 2003, Feng Zhang wrote:

> There is no way to answer this question?
> 
> even for writing the sample covariance matrix
> formulation for the data set [X, Y] where
> X(n observations) and Y (m observations) are from
> the class 1 and class 2 which both are
> multidimensional normal distribution?
> 
> 
> ----- Original Message -----
> From: "Feng Zhang" <f0z6305 at labs.tamu.edu>
> To: "R-Help" <r-help at stat.math.ethz.ch>
> Sent: Tuesday, February 11, 2003 12:11 AM
> Subject: [R] Covariance matrix for GMM
> 
> 
> > Hey, All
> >
> > Now I generate a data vector X (d-dimension column vector) from a Gaussian
> > Mixture Model (GMM).
> > That is, the pdf of vector X is
> > f(X) = a1*N(u1, Cov1) + a2*(u2, Cov2)
> > where a1+a2 = 1, N is multidimensional normal distribution, ui is the mean
> > vecotr, Covi is the covariance matrix, i=1, 2.
> >
> > So can I get the close forms of the mean and covariance matrix for the
> > random vector X?
> >
> > Thanks very much.
> >
> > Fred
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > http://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> http://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 

-- 
318 Carr Hall                                bolker at zoo.ufl.edu
Zoology Department, University of Florida    http://www.zoo.ufl.edu/bolker
Box 118525                                   (ph)  352-392-5697
Gainesville, FL 32611-8525                   (fax) 352-392-3704