[tgb]

I won't dispute the main point of the article but a couple minor errors bug me. First, he kept referring to a Gaussian distribution as being the unit sphere, when of course the radius depends upon the parameters of the Gaussian (the standard deviation). If not, then it wouldn't be invariant under which units you chose. A bizarre mistake to repeat many times throughout the article.

Less importantly, the last paragraph says that the probability that two samples are orthogonal is "very high". Being precisely orthogonal is technically a probability zero event. There author means "very close to orthogonal."

There was a good discussion about this problem in the context of Monte Carlo simulations in (1).

(1) https://arxiv.org/abs/1701.02434

[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.

[kgwgk]

> There was a good discussion about this problem in the context of Monte Carlo simulations in (1).

There was some discussion here about that paper a few months ago:

https://news.ycombinator.com/item?id=13750621

[tgb]

In fact that's where I found it from!