Superb Technical Writing

Every so often, I've been lucky enough stumble a beautiful piece of mathematical exposition that both opens my eyes to new material and inspires me to be a better technical writer. Here are a few books that have had this impact on me; I highly recommend them to all students and researchers in statistics or machine learning.

• Introduction to Probability, Joseph K. Blitzstein and Jessica Hwang

• Understanding Analysis, Stephen Abbott

• Linear Algebra Done Right, Sheldon Axler

• High-Dimensional Probability, Roman Vershynin

• An Introduction to Statistical Learning, Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani

• Plane Answers to Complex Questions: The Theory of Linear Models, Ronald Christensen

• Convex Optimization, Stephen Boyd and Lieven Vandenberghe

Applied Statistics References

When consulting on applied problems, such as when I've lead statistical consulting workshops, there are a few bread-and-butter tools that constantly come up. Here are the references I recommend most often to students as foundational material for doing applied statistics.

Tutorials

• Mixed models tutorial. A quick introduction to mixed effects modeling, with R code included.

General references

• Introduction to Statistical Learning. A very short, quick introduction to statistical learning methods. Because this book doesn't contain much math, it can be read quickly, and it provides a lot of good intuition with very little overhead. Free online from the link provided.

• Elements of Statistical Learning. This is my favorite all-around reference for graduate level applied statistics. Free online from the link provided.

• Plane Answers to Complex Questions. A great (but slightly classical) treatment of linear models. Free for Stanford students from the link provided.

• Categorical Data Analysis. This is a standard text on categorical data analysis.

• Multivariate Analysis. This is the classic text on multivariate analysis.