Earlier quoted context omitted.
> by determining the distribution of the process that the data was generated from. Well, each random variable has a distribution. And there are a few distributions that are common so are taught. Then, presto, bingo, too many students conclude that an important first step is to find a distribution. However, commonly in practice, with just samples and without more in mathematical assumptions, finding a distribution is…
>And made no more than meager, general assumptions about distributions. I don't see how assuming the data are IID from a Gaussian is a meager assumption.
It's not. Somehow we have failed to communicate accurately.
I wrote
> But, with just meager assumptions, commonly can still proceed and know that are still making a best L^2 approximation.
In that sentence, I didn't suggest that those "assumptions" were the Gaussian i.i.d. of the previous paragraph. Instead, I left the "assumptions" unspecified. Why? Because there is quite a variety available. But lots of the options are "meager".
Typically with more assumptions, can get more results. But for model fitting, building, constructing, discovering, whatever, can still get a lot with next to nothing in assumptions.