
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&#x27;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.
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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_.

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lunarcea
Thanks for your help, xelxebar!

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s1t5
Harvard's Stat110 by Joseph Blitzstein and the accompanying book Introduction
to Probability -
[https://projects.iq.harvard.edu/stat110/youtube](https://projects.iq.harvard.edu/stat110/youtube)

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lunarcea
Awesome

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toto444
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.

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lunarcea
Thanks, toto444!

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

Taylor and Karlin, "An Introduction to Stochastic Modeling"

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s1t5
ISL is a good introduction to machine learning which isn't quite what OP is
asking for.

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lunarcea
Great!

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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.

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BOOSTERHIDROGEN
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).

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lunarcea
Thanks!

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sova
Try and visualize everything
[https://github.com/piermorel/gramm](https://github.com/piermorel/gramm)

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lunarcea
Nice thanks!

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

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lunarcea
Thanks

