Agreed, this is extremely well-done. Even worse than the general lack of statistical education, I feel the teaching of statistics and probability suffers of the same problems as calculus/real analysis. Introductory statistics classes ramble at length about how random variables are functions from a probability space to a measurable space, but everyone who actually 'gets' the concept behind it eventually thinks in terms of realizations (i.e. much more similarly to what this tutorial does). Intuition without theory is shallow, but theory without intuition just leads to you eventually forgetting the theory.

I’ll copy my comment from other place in this thread, because I think it might be relevant here. I feel that most math subjects are treated either as full-on “fluff” (e.g. calculus, all computing, no theory building) or full-on theory (real analysis). A combination of intuition AND rigor is hard to come by. With that said...

What textbook(s?) would you recommend for a thorough self-learning of statistics? I’m looking for both intuition _and_ mathematical rigor — not all proofs, but not all fluff either.

I’m a bioinformatics student and I will have a semester of combined probability/stats some time this year, but I think that won’t be enough to support me given my preference for DS-based bioinformatics jobs.

I’m reading Feller right now for the probability stuff, but I’m unsure about statistics. I don’t even know what the relation between probability and statistics is — most similar questions I found online (i.e. “How to learn stats?”) are answered with a “Read this probability book and you’re good”.

> I feel that most math subjects are treated either as full-on “fluff” (e.g. calculus, all computing, no theory building) or full-on theory (real analysis)

My background is computer science and I had a similar experience. Just a caveat: I'm not arguing that we should stop teaching theory, quite the contrary: most of the times we err on the side of the fluff. In particular, the fact that many reputable institutions are cutting formal logic, computability theory, etc. from their CS curriculums is an absolute disgrace. Intuition is hard to teach (easy to fall into the 'monads are burritos' trap) and it's something you have to work for yourself if you want to develop. My point is just that lack of intuition/operative knowledge will lead to your theoretical knowledge of the field being less in-depth and generally less helpful to you.

I honestly don't think it really matters what book you are studying as an introduction to a subject, as usually introductory courses are teaching well-established theory that everyone knows/agrees on. If you have no prior knowledge, a decent starting point is this: https://www.amazon.com/gp/product/1981369198/ the author's website has similar content: https://www.statlect.com

> My background is computer science and I had a similar experience. Just a caveat: I'm not arguing that we should stop teaching theory, quite the contrary: most of the times we err on the side of the fluff.

Bioinformatics at my uni is just the typical CS minus some hardware stuff + molecular biology minus some chemistry stuff; in other words, I'm pretty close to CS, too. And I share your opinion — at least for me, I don't believe things until I see them proven.

> My point is just that lack of intuition/operative knowledge will lead to your theoretical knowledge of the field being less in-depth and generally less helpful to you.

In addition, building an intuition can help make the understanding come faster. To give you an example, I can stare at a proof for half a day and _then_ finally get it, but one clever diagram or a descriptive commentary can save me hours of pushing through the dense text — without cutting down on the rigour (as the proof is still there). Unfortunately, it seems that maths textbooks mostly come only with the former, or the latter, but not both.

> I honestly don't think it really matters what book you are studying as an introduction to a subject

I agree that it probably doesn't matter from the content POV (i.e. the basic definitions and theorems will be there), but it could matter if we take the intuition into account.

For example, in real analysis, there's baby Rudin, but there's also all sorts of books that include all (or most of) the content, but supply it with better commentary and/or illustrations to drive the point home quicker. And I'd day that's a pretty established field, too; probably more so than stats, in fact.

By the way, it seems that statlect focuses a lot on probability and so has quite an overlap with Feller. If you had to choose a primary text you'd read, which one of those two would you take?

I am so glad I am not the only one that feels this way. In high school, I didn't have to take a single probability/stats class. In college, as a CS major (!!), I had to take a single intro stats class that was completely insufficient. And when a stats education is insufficient, god damn is it insufficient. No motivating examples whatsoever (what distribution would I use to measure ${real world process}? why would I need to calculate ${X} about the distribution?), just formulas that you're expected to memorize and vomit onto an exam with no understanding of why you're doing what you're doing at all.

What is the deal with this? Why isn't stats commonly taught in school when it is by far one of the most prevalent disciplines? And why, on the rare occasion when it is taught, is it so abysmal? Statistics forms the basis for all of science, for god's sake. I've since developed a patchwork understanding of statistics on my own from various resources I've found the time to consume. For the record, I grew up in the US.