Track model_logp in other samplers

[eigenfoo]

Following up from #3134. The previous PR only added model_logp for NUTS and HMC. Apart from them, no other sampler computes the logp (e.g. the Metropolis samplers only computes the delta_logp), so there would be overhead to require these samplers to track the logp.

Quoting @junpenglao:

I have an idea to do this also for Metropolis where we are computing the delta_logp instead of the logp. We can compute the model logp at sample 0, then from sample 1 onward we do state.logp = logp_tm1 - delta_logp which should recover the logp at time t while also cheap to compute.

We should decide what samplers should support exporting the logp (i.e. which samplers already do this, or something close to it).

[eigenfoo]

I suggest that we add logp to the following samplers:

• SMC: AFAICT we compute the logp here, and again, just need to percolate that up to the trace.
• Elliptical Slice: it looks like we already compute logp, it's just a matter of percolating that information up to the trace, similar to what I did in Track model logp during sampling #3121
• Slicer: similar to the elliptical slice above.
• Metropolis: the Metropolis samplers compute delta_logp for each sample, so all that is required is to compute the logp for the first step, and then cumulatively sum the delta_logps.

I'm not sure if we could also add the logp to the Gibbs sampler and SGMCMC, or if that would be worthwhile.

cc @junpenglao

[junpenglao]

re Gibbs:
https://github.com/pymc-devs/pymc3/blob/26267ca9ca57c2da4da74b5a230e4913dd6735e1/pymc3/step_methods/metropolis.py#L348

https://github.com/pymc-devs/pymc3/blob/26267ca9ca57c2da4da74b5a230e4913dd6735e1/pymc3/step_methods/metropolis.py#L435

[eigenfoo]

I'm confused, what is the difference between gibbs.py and metropolis.py?

[junpenglao]

the ElementwiseCategorical step in gibbs.py was supposedly deprecated but there is a bug in it or something... I dont remember exactly...

[junpenglao]

OK found the issue: #1563 and #2879

[ricardoV94]

Related to #3546