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I like how pyro from Uber is structured, that it uses pytorch and how many features it brings. Pymc looks ok as well (but would not be my favorite with regards to the syntax and lifetime!)

Do you have a book you would highlight for learning probabilistic programming, the variational inference, ...

I found books using pymc

And the book "Variational Methods for Machine Learning with Applications to Deep Networks" with ~140 pages seems rather short (and the table of contents did not convince me yet).

Do you have suggestions. Should I just go with one of the pymc books? (Although pymc3 will die sooner or later because it is based on theano, which is deprecated - I would prefer a pytorch or Jax based probabilistic programming language)

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    $\begingroup$ (+1) I honestly find it frustrating how the majority of non-trivial examples from PyMC3 tutorials do not work with PyMC5. (And the switch away from Theano to PyTensor isn't the issue, they have changed a lot of other arguments too.) That said Statistical Rethinking (2nd Edition) seems to have NumPyro ports. $\endgroup$
    – usεr11852
    Mar 22, 2023 at 22:40

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I ended up buying "An Introduction to Bayesian Inference, Methods and Computation" by Nick Heard which I felt that it describes the theory quite nice (although some computations become really long). For practical ideas I first read "Probabilistic Programming and Bayesian Methods for Hackers" (see link above).

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