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For Bayesian stats, "Statistical Rethinking" by McElreath is a masterpiece.



This should be the top comment, I'm reading his newly released 2nd edition and it is outstanding. Other mentions are -

  - Doing Bayesian Data Analysis (dog book)
  - Student's Guide to Bayesian Statistics
Slightly more advanced

  - Bayesian Data Analysis 3 (currently free! http://www.stat.columbia.edu/~gelman/book/)




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