[conjectures]

On that point my teeth were grinding because it assumes an identity covariance matrix. Ie the bubble needn't even be spherical.

The second is that the squared norm has a chisq distribution. There's no point simulating it. You can just plot the pdf, and have all kinds of facts about its mean, var, entropy etc. Also, iirc Shannon had something to say about this.

However, I do think these facts are worth a reminder.

[jjoonathan]

I don't (on the first point). Everyone with the background to understand the problem under discussion and appreciate the explanation already understands that Gaussians are parametrized. I challenge you to find a counterexample. The specifics of non-isotropic parametrizations are even less relevant to the discussion than scalar parametrization.

On the second point, I agree that the approximation deserves a mention.