[lupire]

How does an upcoming college student, or worse an already graduate, learn statistics like this, with depth of understanding of the meaning of the math, vs just plug an chugging cookbook formulas and "proving" theorems mechanically without the deep semantics?

[ayhanfuat]

Statistical Rethinking is quite good in explaining this stuff. https://xcelab.net/rm/

[disgruntledphd2]

Basically all of the Andrew Gelman books are also good.

Data Analysis... https://sites.stat.columbia.edu/gelman/arm/ Regression and Other Stories: https://avehtari.github.io/ROS-Examples/

Wasserman's All of Statistics is a really good introduction to mathematical statistics (the Gelman stuff above are more practically and analytically focused).

But yeah, it would probably be easier to find a good statistics course at a local university and try to audit it or do it at night.

[monkeyelite]

Dont take the “for engineers” version.

> and "proving" theorems mechanically

I think you’ve have a bad experience because writing a proof is explaining deep understanding.

[JadeNB]

> I think you’ve have a bad experience because writing a proof is explaining deep understanding.

I think your wording is the key—coming up with a proof is creating deep understanding, but writing a proof very much need not be explaining or creating deep understanding. Writing a proof can be done mechanically, by both instructor and student, and, if done so, neither demonstrates nor creates understanding.

(Also, in statistics more than in almost any other mathematically based subject, while the rigorous mathematical foundations are important, a complete theoretical understanding of those foundations need not shed any light on the actual practice of statistics.)

[alejohausner]

You're right. Coming up with a proof is a creative process. Each major proof in mathematics is so unique, that it usually gets named after its inventor. So we have Euclid's proof that there are infinitely many primes, Euler's proof that e is irrational, and Wiles' proof of Fermat's last theorem.

[monkeyelite]

> need not shed any light on the actual practice of statistics.

That’s not what this comment asked for.

[c7b]

I'd say reading about statistics and being curious is a great start :)