Add warmup iterations and _group_warmup

[ahartikainen]

Description

Implement save_warmup for PyStan.

Adds _groups_warmup to InferenceData.

Warmup groups must start with _warmup_.

Checklist

• Follows official PR format
• New features are properly documented (with an example if appropriate)?
• Includes new or updated tests to cover the new feature
• Code style correct (follows pylint and black guidelines)
• Changes are listed in changelog

[codecov]

Codecov Report

Merging #1126 into master will decrease coverage by 0.12%.
The diff coverage is 87.70%.

@@            Coverage Diff             @@
##           master    #1126      +/-   ##
==========================================
- Coverage   92.70%   92.58%   -0.13%     
==========================================
  Files          93       93              
  Lines        9023     9129     +106     
==========================================
+ Hits         8365     8452      +87     
- Misses        658      677      +19     

Impacted Files	Coverage Δ
arviz/plots/backends/__init__.py	29.11% <ø> (ø)
arviz/rcparams.py	93.10% <ø> (ø)
arviz/utils.py	90.00% <0.00%> (-0.96%)	⬇️
arviz/data/inference_data.py	81.88% <83.01%> (-1.26%)	⬇️
arviz/data/io_pystan.py	98.67% <95.45%> (-0.40%)	⬇️
arviz/plots/backends/bokeh/pairplot.py	75.19% <0.00%> (-1.42%)	⬇️
arviz/data/io_pyro.py	95.86% <0.00%> (-1.37%)	⬇️
arviz/plots/pairplot.py	92.68% <0.00%> (-1.22%)	⬇️
arviz/plots/backends/matplotlib/pairplot.py	70.89% <0.00%> (-0.10%)	⬇️
arviz/plots/densityplot.py	93.33% <0.00%> (+1.66%)	⬆️
... and 2 more

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[ahartikainen]

Hi,

we need to decide on a few things

• is _groups_warmup good way to implement this
• should we show more of the warmup groups in the repr?
• what term is used: warmup, tuning, burn-in (no thanks for burn-in), something other?

[canyon289]

This is look great. Thank you Ari!

[OriolAbril]

Looks good. I figured it could also be of interest to @michaelosthege.

[michaelosthege]

@OriolAbril indeed, thanks!

In PyMC3 we recently added properties to track the number of tuning iterations in the sampler report. (The tune sampler_stat is not always available.)
@ahartikainen Would this be something to consider in arviz.from_pymc3 to automatically splice our traces too?

EDIT: forgot to link pymc-devs/pymc#3827

[ahartikainen]

Yes, pymc should have this too (and other interfaces).

I have used pystan here as a first example.