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Probability and statistics learning recommendations

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This page provides subject-specific learning recommendations for the subject probability. See all our learning recommendations pages |
This page provides subject-specific learning recommendations for the subject statistics. See all our learning recommendations pages |

This page includes recommendations on the closely intertwined subjects of probability and statistics.

Books for self-learning probability and statistics

These books start with a foundation of probability and then use it for statistics. Most of the recommendations include the Bayesian approach, though they may not focus exclusively on this approach.

Book Author(s) ISBN and purchase links Price estimate Who we're recommending it for and why we're recommending it
Probability Theory: The Logic of Science E. T. Jaynes (author), G. Larry Bretthorst (editor; the book was published after Jaynes' death; Bretthorst edited and polished Jaynes' manuscript for publication) ISBN 978-0521592710, Amazon Kindle Kindle edition ~$50, Hardcover ~$100 The book provides a lengthy conceptual and philosophical foundation for probability, albeit one that is not universally accepted. If you're interested a lot in the why and what of probability, rather than simply the execution aspects, this might be the book for you. The book was also the top-voted recommendation and accepted answer to a Math StackExchange question about the best book to learn probability.
Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives (Wiley Series in Probability and Statistics) Andrew Gelman (editor) and Xiao-Li Meng (editor) ISBN 978-0470090435, Amazon Kindle $75-100 The book quickly gets to how to apply probability to the analysis of social and political problems. Cyan's comments in the LessWrong thread about the best textbooks views Gelman favorably in this light compared to Jaynes and Bernardo.
Probability Theory: A Concise Course (Dover Books on Mathematics) Y. A. Rozanov ISBN 978-0486635446, Amazon Kindle $5-10 (both Kindle and paperback available) A relatively low-cost and short introduction to probability of decent quality.