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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