Move predict from Turing

[sunxd3]

This PR aims to move predict function from Turing.jl repo to here (DynamicPPL). This PR won't change the way that predict is fundamentally implemented. (Later in #651, we will transition to using fix to implement predict.)

The challenge of this PR is that:

1. predict returns a MCMCChains.Chain
2. the implementation in Turing.jl uses the Chain generation pipeline in Turing.jl (same pipeline called at the end of sample)
3. it doesn't really make sense to move all the Chain-related util functions into DynamicPPL
4. so we need to separate a subset of the util functions and add to DynamicPPL

What I have done as of now:

1. move the predict function and recovered a subset of the util functions needed to make it functional
2. sample in tests now uses LgoDensityFunction interface

Modifications made to the moved util functions are:

1. AbstractMCMC.bundle_samples are renamed to _bundle_samples; unused keywords arguments are removed
2. Transition type is copied from Turing.jl repo, but the stat field is removed as it is never used in predict

But most of the functions in the PR right now should be the same or straightforwardly identifiable from Turing.jl code.

[sunxd3]

Some tests still fail: the mean of the predictions looks correct, but it seems the variance is high. Not certain where goes wrong, so need further investigation.

The reason is some tests implicitly rely on the variance of the posterior samples. Discarding some initial samples fixes this. Turing do this by default, but via LogDensityFunction we need do the discarding explicitly.

[coveralls]

Pull Request Test Coverage Report for Build 12007336979

Details

• 47 of 48 (97.92%) changed or added relevant lines in 2 files are covered.
• 25 unchanged lines in 4 files lost coverage.
• Overall coverage increased (+0.2%) to 84.55%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
ext/DynamicPPLMCMCChainsExt.jl	34	35	97.14%

Files with Coverage Reduction	New Missed Lines	%
src/model.jl	1	94.44%
src/varinfo.jl	6	86.3%
src/simple_varinfo.jl	6	86.6%
src/threadsafe.jl	12	57.76%

Totals
Change from base Build 11934706726:	0.2%
Covered Lines:	3601
Relevant Lines:	4259

---

💛 - Coveralls

[codecov]

Codecov Report

Attention: Patch coverage is 97.91667% with 1 line in your changes missing coverage. Please review.

Project coverage is 84.55%. Comparing base (ba490bf) to head (53b6749).

Files with missing lines	Patch %	Lines
ext/DynamicPPLMCMCChainsExt.jl	97.14%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #716      +/-   ##
==========================================
+ Coverage   84.35%   84.55%   +0.19%     
==========================================
  Files          30       30              
  Lines        4211     4259      +48     
==========================================
+ Hits         3552     3601      +49     
+ Misses        659      658       -1     

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[sunxd3]

We had a fast discussion on this today at the meeting. Tor raised that we should probably implement predict that take generic Vector as the second argument (instead of just Chain), this is because predict works with sample, and sample can produce non-Chain type returns.

Also although we don't use fix for this PR yet, it is worthwhile to have some nice and better thought-out implementations.

[torfjelde]

Vector as the second argument

Specifically, I was thinking Vector{<:VarInfo}:) But otherwise, this sounds very good 👍

[torfjelde]

Do we really need the PredictiveSample here?

My original suggestion was just to use Vector{<:OrderedDict} for the return-value (an abstractly typed PredictiveSample doesn't really offer anything beyond this, does it?)

[sunxd3]

I haven't think too deep about this. A new type certainly is easier to dispatch on, but may not be necessary. Let me look into it

[torfjelde]

Otherwise stuff is starting to look nice though:)