Peter:
You overcounted the number of "INDEPENDENT" parameters.
The no. of independent mixing proportions for a k component mixture is k-1,
in this case of a 3-component mixture, only two independent mixing
proportions
p1, p2, (since p3=1-p1-p2).
Cheers.
Jose Ramon G. Albert, Ph.D.
Chief, Research Division
Statistical Research and Training Center
www.srtc.gov.ph
104 Kalayaan Ave., Diliman, Quezon City
PHILIPPINES
----- Original Message -----
From: Peter Austin <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, May 16, 2000 4:16 AM
Subject: singular covariance matrix
> Dear users group,
> I am using BUGS to fit a mixture of three Normal distributions to a
dataset
> of 82 observations (Chib's data of velocities of galaxies, appearing in
JASA,
> 1995, Vol 90, p1313-1321). I am fitting a mixture of three Normals, all
with
> the same variance. The resulting model has 7 parameters (three means, one
> variance, and the three mixing proportions). The Gibbs sampler appears to
> converge and move around the sampling space. I received parameter
estimates
> similar to those appearing in the literature using the same data (allowing
for
> differences in prior distributions). I have done a variety of convergence
> diagnostics, and the model appears appropriate. I allowed the sampler to
run
> for 1000 iterations, after allowing it to burn in for 1000 iterations.
> However when I calculate the 7x7 variance-covariance matrix of the 1000
> sampled values of the 7 parameters, it is singular. I had wanted to use
the
> determinant of this matrix in a computation. There did not appear to be a
> high degree of autocorrelation or cross-correlation in the sampled values.
> Can someone explain to me what could have caused the variance matrix to be
> singular?
>
> Thanks,
>
> Peter
>
>
> Peter Austin, PhD
> Institute for Clinical Evaluative Sciences
> Ontario, Canada
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