One of the best-known books on statistics is now free
Larry Wasserman’s All of Statistics is free to download from Springer
I like this book because – unlike most books on statistics – it takes a modern approach to statistics and covers statistics and computer science holistically.
In doing so, it covers a much broader range of topics (hence the name).
However, the book is also quite readable because the author says ‘Rigor and clarity are not synonymous’
Hence, it strikes a good balance
Part I is concerned with probability theory
Part II is about statistical inference, data mining and machine learning.
Part III applies the ideas from Part II to specific problems such as regression, graphical models, causation, density estimation, smoothing, classification, and simulation.
Admittedly, seeing everything in terms of statistics needs some getting used to
- Regression is a method for studying the relationship between a response variable Y and a covariate X. The covariate is also called a predictor variable or a feature. One way to summarize the relationship between X and Y is through the regression function
- Classification can be seen as the problem of predicting a discrete random variable Y from another random variable X
- Gaussian and Linear Classifiers : Gaussian and Linear Classifiers use the density estimation strategy and assume a parametric model for the densities.
- Trees are classification methods that partition the covariate space X into disjoint pieces and then classify the observations according to which partition element they fall in.
Etc etc …
The link again to download is
Larry Wasserman’s All of Statistics