Metropolis chain tuning is differs between single- and multiprocessing

[michaelosthege]

(split from #3731)

Observations

When Metropolis is used with cores > 1 and chains > 1, all chains are independently tuned.

With cores=1 however, Metropolis initializes the 2nd chain with the scaling from the first. It is still tuned, but in the end it's a different between sequential single-process and parallelized multiprocess sampling.

Cause

For Metropolis, the stepper is re-used and re-tuned, but no reset happens.

https://github.com/pymc-devs/pymc3/blob/dc9fd7251b34e9851308e91d622513ebe648f49e/pymc3/sampling.py#L711-L716

Possible Solutions

• re-setting the tuning parameter before continuing with the next chain
• ...other ideas?

[ColCarroll]

Wow, this is interesting.

1. This is definitely a bug, in that it is different behavior due to settings that have nothing to do with tuning. I think we should reset the tuning parameter (or just initialize a new stepper?) before continuing.
2. More generally, sharing tuning data between chains does not seem like a bad idea to me, either as an early diagnostic (if you just compare them), or to speed up tuning (like here, we have a "good initialization" for scaling).

[michaelosthege]

Over in #3784 I fixed it for the DEMetropolisZ. Shall I include a fix for Metropolis in the same PR ?

[junpenglao]

I think it is better sending a separate PR.