[jampekka]

Not everything is a linear combination of large number of (IID) samples, and thus not everything is gaussian distributed.

[kgwgk]

You’re implying that many things are though.

[jampekka]

Yes, and I was explicit about it in another comment in this post.

[kgwgk]

Ok, so we all agree that in most cases the reason to minimize square error is that it’s the appropriate thing to minimize - not that it has an analytical solution, convenience or tradition.