Free statistical textbooks Are there any free statistical textbooks available? 
 A: Cosma Shalizi, CMUs ML guru, occasionally updates a draft of a stats book soon to be published by Cambridge Press titled Advanced Data Analysis from an Elementary Point of View. Can't recommend it highly enough...
Here's the Table of contents:
I. Regression and Its Generalizations
Regression Basics
The Truth about Linear Regression
Model Evaluation
Smoothing in Regression
Simulation
The Bootstrap
Weighting and Variance
Splines
Additive Models
Testing Regression Specifications
Logistic Regression
Generalized Linear Models and Generalized Additive Models
Classification and Regression Trees 

II. Distributions and Latent Structure
Density Estimation
Relative Distributions and Smooth Tests of Goodness-of-Fit
Principal Components Analysis
Factor Models
Nonlinear Dimensionality Reduction
Mixture Models
Graphical Models 

III. Dependent Data
Time Series
Spatial and Network Data
Simulation-Based Inference 

IV. Causal Inference
Graphical Causal Models
Identifying Causal Effects
Causal Inference from Experiments
Estimating Causal Effects
Discovering Causal Structure 

Appendices
Data-Analysis Problem Sets
Reminders from Linear Algebra
Big O and Little o Notation
Taylor Expansions
Multivariate Distributions
Algebra with Expectations and Variances
Propagation of Error, and Standard Errors for Derived Quantities
Optimization
chi-squared and the Likelihood Ratio Test
Proof of the Gauss-Markov Theorem
Rudimentary Graph Theory
Information Theory
Hypothesis Testing
Writing R Functions
Random Variable Generation

A: Some free Stats textbooks are also available here.
A: It's nice to see academics freely distribute their works. Here is trove of free ML / Stats books in PDF:
Machine Learning


*

*Elements of Statistical Learning Hastie, Tibshirani, Friedman

*All of Statistics Larry Wasserman

*Machine Learning and Bayesian Reasoning David Barber

*Gaussian Processes for Machine Learning Rasmussen and Williams

*Information Theory, Inference, and Learning Algorithms David MacKay 

*Introduction to Machine Learning Smola and Vishwanathan

*A Probabilistic Theory of Pattern Recognition Devroye, Gyorfi, Lugosi

*Introduction to Information Retrieval Manning, Rhagavan, Shutze

*Forecasting: principles and practice Hyndman, Athanasopoulos (Online Book) 
Probability / Stats


*

*Introduction to statistical thought Lavine

*Basic Probability Theory Robert Ash

*Introduction to probability Grinstead and Snell

*Principle of Uncertainty Kadane
Linear Algebra / Optimization


*

*Linear Algebra, Theory, and Applications Kuttler

*Linear Algebra Done Wrong Treil

*Applied Numerical Computing Vandenberghe

*Applied Numerical Linear Algebra James Demmel

*Convex Optimization Boyd and Vandenberghe
Genetic Algorithm


*

*A Field Guide to Genetic Programming Poli, Langdon, McPhee

*Evolved To Win Sipper

*Essentials of Metaheuristics Luke
A: Online books include

*

*http://davidmlane.com/hyperstat/

*http://vassarstats.net/textbook/

*http://www.psychstat.missouristate.edu/multibook2/mlt.htm

*http://bookboon.com/uk/student/statistics

*http://www.freebookcentre.net/SpecialCat/Free-Statistics-Books-Download.html
Update: I can now add my own forecasting textbook

*

*Forecasting: principles and practice (Hyndman & Athanasopoulos, 2012)
A: Statsoft's Electronic Statistics Handbook ('The only Internet Resource about Statistics Recommended by Encyclopedia Britannica') is worth checking out.
A: I know other authors have gone to some trouble to make their books available here on stack exchange ...  The printed version of our 2002 edition was printed 3 times and sold out 3 times;  Springer and Google recently started selling it (book only) as a PDF eBook (no software) on the Springer and Google sites for $79.
We are delighted to be able to make the PDF eBook version (2002 edition) available for FREE to stackexchange users at: 
http://www.mathstatica.com/book/bookcontents.html

This is a complete PDF version of the original 2002 printed edition. Although no software is included (neither Mathematica nor mathStatica), the methods, theorems, summary tables, examples, exercises, theorems etc are all useful and relevant ... even as a reference text for people who do not even have Mathematica. 
One can either download:


*

*the entire book as a single download file ... with live clickable Table of Contents etc,  ... or

*chapter by chapter.
iBooks installation
To install as an iBook:


*

*Download the entire book as a single PDF file

*Then drag it into iBooks (under the section: PDF files).
iPad installation
To install on an iPad: 


*

*First install it as an iBook (as above)

*Open iTunes; select your iPad; click on Books: select the book and sync it over to your iPad. 
A: The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is a standard text for statistics and data mining, and is now free:
https://web.stanford.edu/~hastie/ElemStatLearn/
Also Available here.
A: Not properly an entire textbook, but the part IV of Mathematics for Computer Science is about probability and random variables.
A: Some downloadable notes on probability, which seems interesting:
http://www.math.harvard.edu/~knill/teaching/math19b_2011/handouts/chapters1-19.pdf
Applied probability:
http://www.acsu.buffalo.edu/~bialas/EAS305/docs/EAS305%20NOTES%202005.pdf
http://www.ma.huji.ac.il/~razk/Teaching/LectureNotes/LectureNotesProbability.pdf
A: A write up of probability tutorials and related puzzles along with R code for learning. Hope it helps
A: http://www.probabilitycourse.com/ is a website hosting free online-based Probability and Statistics textbook. It also has extra features such as graphing tools and lecture videos
A: Here is also a great free book on multivariate statistics by Marden, primarily concerned with the normal linear model linked on this page:
http://istics.net/stat/pages/Statistical%20education/Statistics%20text%20books-%20Free%20and%20not%20free.html
A: Gelman et al. "Bayesian Data Analysis" (3rd edition).

A: Introduction to Statistical Thought
A: There's a superb Probability book here:
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
which you can also buy in hardcopy.;
A: I've often found the Engineering Statistics Handbook useful. It can be found here.
Although I've never read it myself, I hear Introduction to Probability and Statistics Using R is very good. It's a full ~400 page ebook (also available as an actual book). As a bonus, it also teaches you R, which of course you want to learn anyways.
A: It's not a textbook but Bayesian Methods in the Search for the MH370 is a great introduction to particle filters. 
A: I really like  The Little Handbook of Statistical Practice by Gerard E. Dallal
A: Machine Learning

*

*One the most, if not the most, popular textbooks on machine learning is  Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning, which is fully available online (currently 10th printing). It is comparable in scope e.g. to Bishop's Pattern Recognition and ML or Murphy's ML, but those books are not free, while ESL is.


*Hastie & Tibshirani also co-wrote freely available An Introduction to Statistical Learning, With Applications in R which is basically a simpler version of The Elements and focuses on R.


*In 2015, Hastie & Tibshirani co-authored a new textbook Statistical Learning with Sparsity: The Lasso and Generalizations, also available online. This one is quite a bit shorter and focuses specifically on lasso.


*Another freely available all-encompassing machine learning textbook is David Barber's Bayesian Reasoning and Machine Learning. I did not use it myself, but it is widely considered to be an excellent book.
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Switching now to more specialized topics, there are:

*

*Rasmussen & Williams Gaussian Processes for Machine Learning, which is the book on Gaussian processes.


*Much awaited Goodfellow, Bengio and Courville Deep Learning textbook that is about to be published by MIT Press. It isn't published yet, but the book is already available online. On the official website one can view it in browser but cannot download (as per agreement with the publisher), but it is easy to find a combined PDF e.g. here on github.


*Csaba Szepesvári, Algorithms for Reinforcement Learning, a concise book on RL. A classical, much more detailed but a bit dated textbook is Sutton & Barto, Reinforcement Learning: An Introduction which is also freely available online but only in a cumbersome HTML format.


*Boyd and Vandenberghe, Convex Optimization.
$\hskip{4em}$



A: Here's a fresh one: Introduction to Probability and Statistics Using R . It's R-specific, though, but it's a great one. I haven't read it yet, but it seems fine so far...
A: A New View of Statistics by Will G. Hopkins is great! It is designed to help you understand how to understand the results of statistical analyses, not how to prove statistical theorems. 
A: Norman Matloff has written a mathematical statistics textbook for computer science students that's free.  Kind of a niche market, I suppose.  For what it's worth, I haven't read it, but Matloff has a Ph.D. in mathematical statistics, works for a computer science department, and wrote a really good R book, that I recommend for people who want to go to the next stage of programming R better (as opposed to just fitting models with canned functions).
A: OpenIntro Statistics
http://www.openintro.org/stat/textbook.php
Inexpensive paperback copies are also available on Amazon.
A: Not Statistics specific, but a good resource is:  http://www.reddit.com/r/mathbooks
Also, George Cain at Georgia Tech maintains a list of freely available maths texts that includes some statistical texts.  http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html
A: "An Introduction to Statistical Learning with Applications in R" http://www-bcf.usc.edu/~gareth/ISL/ by two of the 3 authors of the well-known "The Elements of Statistical Learning" plus 2 other authors.  An Introduction to Statistical Learning with Applications in R is written at a more introductory level with less mathematical background required than The Elements of Statistical Learning, makes use of R (unlike The Elements of Statistical Learning), and was first published in 2013, some years after this thread was started.
A: I really like these two books by Daniel McFadden of Berkeley:

*

*Lecture Notes: Econometric Tools
http://elsa.berkeley.edu/users/mcfadden/e240a_sp98/e240a.html


*Lecture Notes: Econometrics/Statistics  http://elsa.berkeley.edu/users/mcfadden/e240b_f01/e240b.html
A: For getting into stochastic processes and SDEs, Tom Kurtz's lecture notes are hard to beat.  It starts with a decent review of probability and some convergence results, and then dives right into continuous time stochastic processes in fairly clear, comprehensible language.  In general it's one of the best books on the topic -- free or otherwise -- I've found.
A: A digital textbook on probability and statistics by M. Taboga can be found at https://www.statlect.com The level is intermediate. It has hundreds of solved exercises and examples, as well as step-by-step proofs of all the results presented.
