Probability and Statistics

Also see: Statistics with Python

Parametric Statistics and Probability

Ross, S. (2021) Introduction to Probability and Statistics for Engineers and Scientists, Sixth edition.; Elsevier, 2021.

Get the sixth edition, especially if you're buying in India. It's excellent and relatively cheap (~INR. 800, August 2025). Also, this edition provides code examples in R, a welcome change.

MIT RES.6-012 Introduction to Probability, Spring 2018

A YouTube playlist with beginner friendly lectures by John Tsitsiklis and Patrick Jaillet from MIT. They also wrote a book on probability and made a summary of it freely available.

Holmes, S., Huber, W. (2019). Modern statistics for modern biology. Cambridge university press. (Free online copy)

Neat, with a particularly nice discussion on the confidence intervals.

Vershynin, R. Undergraduate Probability (2022) and High-Dimensional Probability (2022)

Both links are YouTube playlists of online courses taught during the pandemic.

Roback P., Legler, J. (2021) Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R

Free online book.

Pishro-Nik, H. (2014) Introduction to Probability, Statistics, and Random Processes

Online book.

Blackwell, M. A User’s Guide to Statistical Inference and Regression

Gelman, A., Hill, J., Vehtari, A. Regression and Other Stories

Guidelines on when not to use regression.

The Book of Statistical Proofs by Joram Soch and collaborators

An open book on GitHub

Non-parametric methods

Garfinkel, A.; Guo, Y. (2026) Understanding Data: A 21st Century Approach to Statistics and Data Science Springer

Unusual book emphasizing a resampling-based nonparametric computational approach over traditional parametric one. The authors have and express strong opinions -- and I don't agree with them at times -- but this is a really well-written and useful book, especially if you're interested in using statistics in your work. Highly recommended.

Shalizi, C. R. (2026) Advanced Data Analysis from an Elementary Point of View. Free PDF

Shalizi writes well and knows what he is talking about (something not as common as you might expect). Check the chapter on Bootstrapping, for example, for more clarity on resampling-based approach.