Kolmogorov's Foundations of the Theory of Probability is pretty good, IMO. I haven't made it very far, but he has great examples, plenty of rigor, and the book is like $10.
Ask HN: What are your favorite statistics and probability textbooks?
11–20 of 87 posts
Re: Ask HN: What are your favorite statistics and probability textbooks?
#12I'm not well rounded enough to draw a clear path from where you are. For me Gelmans Data Analysis Using Regression and Multilevel/Hierarchical Models [0] drove home many, many points. More recently, I have a sense/hope that Pearl's The Book of Why [1] might take this to yet another level.
[0] http://www.stat.columbia.edu/~gelman/arm/ [1] https://www.amazon.com/Book-Why-Science-Cause-Effect/dp/0465...
Re: Ask HN: What are your favorite statistics and probability textbooks?
#13I've been enjoying the struggle through Statistical Inference by George Casella as a foundational text. This was the introductory text for stats graduate students at Arizona State University a few years back.
The Mathematical Methods of Statistics by Harald Cramér is also excellent.
Re: Ask HN: What are your favorite statistics and probability textbooks?
#14casella and burger is the standard grad math stats book and good-ish departments i.e. it proves things using calculus but it's for statisticians (covers things like efficiency and biasedness and etc).
Re: Ask HN: What are your favorite statistics and probability textbooks?
#15FWIW here is a list of texts used in a data science conferene as references in presenter's slides (Cassella Berger was mentioned here by others, Hastie Tibshirani is also good). https://hastebin.com/raw/upiqumenas
Re: Ask HN: What are your favorite statistics and probability textbooks?
#16"Theory of Probability" by Bruno de Finetti is the best text on probability ever written.
Re: Ask HN: What are your favorite statistics and probability textbooks?
#17Feller Vol. 1 is considered the classic text for discrete probability: https://epubs.siam.org/doi/10.1137/1011021 Volume 2 is easily found as a pdf on google, but it's much harder.
Feller is damn hard work. I'd put feller's probability on the same level as Rudin's real analysis.
Re: Ask HN: What are your favorite statistics and probability textbooks?
#18All of Statistics by Larry Wasserman is the book I recommend for anyone who knows calculus and linear algebra and wants to learn statistics.
Came here to post this and “Advanced Data Analysis from an Elementary Point of View“ by Cosmos Shalizi
Re: Ask HN: What are your favorite statistics and probability textbooks?
#19[deleted]
Re: Ask HN: What are your favorite statistics and probability textbooks?
#20A great starting book that helps build a good intution is "An Introduction to Error Analysis" by John Taylor (of Classical Mechanics fame). Basically if you are taking any kind of measurements and need to compose them intelligently this is where to start. From sig-figs to chi squared. A must read for any starting researcher
My experience otherwise with stats books has been horrendous.. (havent found a good "medium level" book to move on to yet)