Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference (Addison-Wesley Data & Analytics)

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...

This is the "online" (abridged) version of this book:

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

There's a full version of another good book ("Think Bayes: Bayesian Statistics in Python") available as a PDF from the publisher here:

https://www.amazon.com/Think-Bayes-Bayesian-Statistics-Pytho...