[scikit-learn] Possible bug in BayesianGaussianMixture?

[Stefan Ulbrich]

Hello,

I think I might have found a bug in the BayesianGaussianMixture–or at least
encountered a behavior that I was not expecting. The problem occurs when
having clusters with small extent (in my case, it is 2D geographic data)
that are far away from each other. While the means and their number are
determined correctly, the co-variance matrices are not (at least compared
to the regular GMM): They are are much wider and point towards the mean of
the cluster centers.
A minimal example and visualization can be seen on a stackoverflow question
I opened.

https://stackoverflow.com/q/54524283

So my question is whether the results of GMM and BGMM should be similar or
this is the expected behavior (and why)?

Thanks in advance for an answer and best wishes
Stefan
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