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I love Julia, but I think comparing Pyro with Turing is pretty unfair.

Pyro can scale to pretty big datasets thanks to custom inference via guides. So you can do inference on pretty sophisticated models such as Deep Markov.

Whereas Turing is mostly for small or medium sized models. For learning purposes, for smaller models or for non-parametrics Turing might be a much better choice, though.

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But isn’t the good scaling due to using variational inference rather than full MCMC? Turing has VI too.

Not just that. Aside from the fact that Pyro has a lot of guide tooling, you get for example (hybrid) message passing for HMMs. This is crucial to scale beyond toy data.

Within Julia, ForneyLab.jl is quite cool for non-deep state space models. I also like Turing.jl, but it has different tradeoffs.

the "good scaling" is due to variational inference, which turns inference problems into optimization problems, but one has to verify the variational approximation holds, etc.

In my experience, Pyro (generally variational inference) is more like a Bayesian optimization than full inference, since it will simply miss multimodality or non-Gaussian tails, etc.

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