[roenxi]

Rather than a textbook, I've had success getting a copy of the course notes directly from the stats department. The best textbooks I've read where history of statistics and philosophy of statistics.

> I’m reading Feller right now for the probability stuff, but I’m unsure about statistics.

Probability is the study of mathematical objects, and nobody is totally sure if any of them exist even in the approximate. Is anything in the universe random? The question is open, and likely to eternally remain so. Lots of things look similar to a random variable if viewed from the right perspective, but most of them aren't actually random. Not really a problem for the mathematicians, they feel no special need to study things that exist.

Statistics is roughly the study of how to deal with actual results. If you do a census, those results exist. Statisticians then need to make decisions about how to think about their results, and usually fall back on models rooted in probability. Technically speaking, "a statistic" is "any quantity computed from values in a sample". [0]

Basically, statistics is probability + data.

[0] https://en.wikipedia.org/wiki/Statistic

[ayewo]

Can you explain this sentence a bit more: "The best textbooks I've read where history of statistics and philosophy of statistics." ?

Are these names of actual books (Google doesn't help) or merely the themes of the stats textbooks you benefited from the most?

Thank you.

[jmalicki]

Not the above poster, but I concur, and recommend Jaynes' "Probability: the logic of science" for the philosophy and history, and "Breakthroughs in statistics" volumes 1 and 2 for the history as told through original foundational papers, from the 1700s on.

[tauist]

Probability Theory is a branch of mathematics. Statistics is the art of processing data to extract information suitable for the human cognitive system or a computer algorithm. Statistics use mathematical tools like physics or chemistry do.