Gibbs Conditionals (new PR)

[phipsgabler]

This is just the same as #1172, but I did some bad things with Git there, so creating a new PR seemed easier

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Introduces a sampler GibbsConditional that can be used to manually specify a -- surprise! -- Gibbs conditional for a variable:

sample(model, Gibbs(GibbsConditional(:λ, cond_λ), GibbsConditional(:m, cond_m)), N)

See also this discussion.

where the cond_v are functions from a NamedTuple of the conditioned variables ((λ,) for m and vice versa in the above example) to a Distribution (or probably just a Sampleable is enough). Example code.

Currently, only one variable per sampler object is handled (as opposed to some other samplers). Of course extension is possible, but I believe it is better to leave it this way and let Gibbs handle the sweeps.

Since this seemed too simple, I'm quite sure there's work left. At least:

• There's a lot of stuff (esp. assume/observe.) simply copied from MH -- can this be simplified or at least abstracted?
• Documentation!
• Tests, naturally
  • Basic feasibility (gdemo, mixture of Gaussians)
  • Check whether indexed variables really work
  • Mixing Gibbs conditionals with other samplers
• Doctests (discuss first)

Currently, the code is working on the tests when only the conditionals or a combination of conditioals and MH is used, but fails in combination with an HMC sampler due to some AD things I don't understand.

[cpfiffer]

The question is also if we want to merge this PR or #1428 (updates Turing to AbstractMCMC 2 which has a different interface and hence requires different implementations of GibbsConditional) first. I have a deadline tomorrow but will try to finish the other PR (and the corresponding one to DynamicPPL) on Wednesday this week.

I would say this one first since it's "smaller" in that it touches less of the code base.

[phipsgabler]

Should be fine now; there's still some issue with variable subsumption, but @trappmartin agreed that I should merge already. I'll make a separate issue.

[devmotion]

You forgot to bump the version number - can you fix this in a new PR? 🙂