docs: Rhats show bad sample quality in several places in the documentation

[DoktorMike]

As of version 0.35 the rhats in https://turinglang.org/docs/tutorials/docs-12-using-turing-guide/#sampling-from-a-conditional-distribution-the-posterior are quite problematic and I see this in many places in the Turing documentation. Given the simplicity of these models it really should be possible to get better samples than this.

I have not tried to sample them myself though. Just reporting what I see in the docs. :)

[penelopeysm]

Hello! Thanks for reporting 😄 they are quite bad indeed. It's just a case of fixing the HMC parameters, or probably just using NUTS() instead.

[yebai]

This example illustrates how to use the most basic HMC sampler without any adaption. As @penelopeysm describes, the current HMC setup is poor, leading to poor mixing. #570 should fix this.

@penelopeysm, can you help go through all examples and create an issue for doc examples with poor mixing? I will help improve the MCMC setup.