Re:Statistical Computing for Scientists and Engineers
by radford-neal on Sunday December 31, 2017 @10:58AM
(#16041007)
I wouldn't recommend learning Lesbegue integration, and so forth, as a starting point for getting to know more about statistics than the canned procedures you may have been exposed to. That is math, not statistics. It's useful once you get to a certain level, but is not essential for learning the concepts. And it's actually detrimental if it gives you the idea that learning more math (beyond first-year calculus and linear algebra) is the road to statistical understanding.
Re:Statistical Computing for Scientists and Engineers
by nabla9 on Sunday December 31, 2017 @11:21AM
(#16041105)
The OP asked about fundamentals and rigor.
There is two ways to learn statistics. Statistical intuition vs. learning the core concepts. When probability is formulated using measure theory things really click together with the rest of the mathematics.
> That is math, not statistics.
Sometimes in the university level statistics department teaches applied statistics and you need to go mathematical department to learn mathematical statistics. What you think is 'real' statistics for you is matter of opinion, but non-applied statistics is pure abstract mathematics.
Re:Statistical Computing for Scientists and Engineers
by radford-neal on Sunday December 31, 2017 @11:25AM
(#16041121)
It's a mistake to think you're learning statistics when you're learning about measure theory, just like it's a mistake to think you're learning physics when you're learning about differential equations. The mathematical tools used in a subject are not the same as the subject itself.
You are half correct. Something is intentionally hidden, but it's not the lack of real content.
The real stuff is called 'Mathematical Statistics' and what you learn in school is 'Statistic's for Scientists and Engineers' or 'Applied Statistics'.
Statistics loos to you random because it's useful everywhere and it must be taught to so many people in other fields. You get a basic set of per-selected tools that are useful and the real stuff is hidden.
If you really want to spend the time and effort to see it as fundamental from ground up, you have to learn mathematic background like set theory, Borel sets, Lebesque measures and integrals, Fourier integrals, etc. Then you start working up from fundamental axioms of random variables. The payday for practically oriented mind comes later and learning it may not be as motivating.