As I said there, I think there are issues with VBGMM. The variational updates are non-standard. There is another issue here: #2454

Does the above code run for you? Which version of scikit-learn are you using?

I think it should be

import numpy as np
import numpy.random as rndn
import sklearn.mixture as skmix
import matplotlib.pyplot as plt
rnd  =  np.random.RandomState()

X = rnd.randn(0.7 * 300, 1) - 5
X = np.vstack((X, rnd.randn(0.3 * 300, 1) * 0.3 + 3))

# gmm = skmix.GMM(2)
gmm = skmix.DPGMM(2)
gmm.fit(X)

x = np.linspace(-10, 10, 1000).reshape(-1, 1)
p = np.exp(gmm.score_samples(x)[0])

plt.hist(X, bins=50, normed=True)
plt.plot(x, p)
plt.show()

integral = np.sum(p) * (x[1] - x[0])
print integral

Both the code above and the code you wrote run (though there's a typo in the import numpy.random statement). I'm using 0.15.2. Both produce the same result. Bad fits and non-normalised predictions.

I only pretty recently looked into the module and I agree that there is something fishy.
I think we need to rewrite it, as the derivation of the variation updates seems non-standard. Any help is very welcome.

I'm currently busy with a job, but I'll have some free time in April. Should be an interesting project - I'll get in touch nearer that time.

We might pose it as a GSOC project, but if no-one takes it you are very welcome. I think it is actually fun, but I'm not sure I'll have the time.

This should be fixed in the new BayesianGaussianMixture class.