Ask HN: Recommend Books on Statistics

[lunarcea]

My PhD in information systems will start this September. Even though I took a class of statistics during Master's, I think I should familiarize myself with probability, stochastic processes, mathematical statistics, and multivariate analysis. Any advice for self studying books regarding these areas would be greatly appreciated.

[xelxebar]

Probability Theory: The Logic of Science (2003) by E. T. Jaynes

This is a treatise on modern probability theory. In the first few chapters, Jaynes quite succinctly derives the theory as what would seem at first blush like a mild extension of binary logic. The whole thing is a bit of a tome but the chapters are not ordered in a strict logical manner, so you can skip around after the first derivation part.

The whole book is gold, though. In my experience, a lot of texts are organized as "statistical toolbags" whereas Jaynes hammers in the point that there are solid principles underlying the theory that, when kept clearly in mind, quickly empower you to approach even tricky problems.

There is even an entire chapter devoted to dispelling "probability paradoxes" which arise from the (mis)use of infinite sets. Jaynes clears these up neatly, making a strong case for always using clearly-defined limiting processes when dealing with non-finite systems.

The foundations presented in this book do stand in opposition to the standard approach using Kolmogorov Axioms. Jaynes' approach is inherently finitistic, which IMHO, makes the reasoning a whole lot more obvious.

[lunarcea → xelxebar]

Thanks for your help, xelxebar!

[s1t5]

Harvard's Stat110 by Joseph Blitzstein and the accompanying book Introduction to Probability - https://projects.iq.harvard.edu/stat110/youtube

[lunarcea → s1t5]

Awesome

[_solr]

All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman

You can find in PDF by typing it into your favorite search engine.

[lunarcea → _solr]

Thanks, _solr!

[Mxtetris]

James, Witten, Hastie, and Tibshirani, "An Introduction to Statistical Learning." Available for download: http://faculty.marshall.usc.edu/gareth-james/ISL/

Taylor and Karlin, "An Introduction to Stochastic Modeling"

[s1t5 → Mxtetris]

ISL is a good introduction to machine learning which isn't quite what OP is asking for.

[lunarcea → s1t5]

Great!

[lunarcea → Mxtetris]

Thanks, Mxtetris!

[jtcond13]

My personal favorite is Richard McElreath's "Statistical Rethinking", which covers regression and multilevel modeling from a Bayesian approach but doesn't assume too much formal math background.

[BOOSTERHIDROGEN → jtcond13]

is there any introduction before this books, I've read first chapter (looking from first chapter, I already have a feeling this is a good book) and author saying there is a substantial idea that is missing from a lot of introduction statistics books (isn't necessarily wrong).

[lunarcea → BOOSTERHIDROGEN]

Thanks!

[lunarcea → jtcond13]

Thank you, jtcond13!

[sova]

Try and visualize everything https://github.com/piermorel/gramm

[lunarcea → sova]

Nice thanks!

[natalyarostova]

Statistical Inference by Casella & Berger, is the canonical first year phd stats textbook. I like it.

[lunarcea → natalyarostova]

Thanks