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Bayesian Data Analysis by Andrew Gelman

http://www.stat.columbia.edu/~gelman/book/

one vote for BDA. For programmers who learn better by implementing things, this book [1] is also good:

[1]: https://www.amazon.com/Bayesian-Methods-Hackers-Probabilisti...

Parts of that book are available online[1] for free. If not for that book I would never have understood how to apply Bayesian stats to problems that interested me.

[1] http://camdavidsonpilon.github.io/Probabilistic-Programming-...

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