adding meaningful str representations to PyMC3 objects

[Spaak]

This is the second PR of three as discussed in #3956 (and likely the one that should get closest attention).

This PR adds semantically meaningful implementations of __str__ to all Distribution, Model, and PyMC3Variable instances, mirroring the already existing functionality for rendering such objects as LaTeX in the context of jupyter notebooks.

Specifically:

model = pm.Model()
with model:
    mu = pm.Normal('mu', mu=0, sd=10)
    sd = pm.HalfNormal('sd', sd=10)
    datobs = pm.Normal('datobs', mu=mu, sd=sd, observed=np.random.normal(size=100))


>>> print(model)
    mu ~ Normal(mu=0.0, sigma=10.0)
    sd ~ HalfNormal(sigma=10.0)
datobs ~ Normal(mu=mu, sigma=f(sd))


>>> print(mu)
mu ~ Normal(mu=0.0, sigma=10.0)

etc.

Of special attention here is that in several places throughout the code str(var) was used to get the name of a variable, for use e.g. in a dict. I've replaced these uses with a new get_var_name function that delegates to TensorVariable.__str__. After merging this PR, future cases where a variable name is required should use get_var_name instead of str.

@twiecki @ColCarroll

[codecov]

Codecov Report

Merging #4076 into master will increase coverage by 0.35%.
The diff coverage is 92.10%.

@@            Coverage Diff             @@
##           master    #4076      +/-   ##
==========================================
+ Coverage   88.29%   88.64%   +0.35%     
==========================================
  Files          88       88              
  Lines       13860    13881      +21     
==========================================
+ Hits        12237    12305      +68     
+ Misses       1623     1576      -47     

Impacted Files	Coverage Δ
pymc3/model_graph.py	88.48% <50.00%> (ø)
pymc3/tuning/scaling.py	58.18% <50.00%> (+0.77%)	⬆️
pymc3/distributions/distribution.py	94.42% <75.00%> (+1.62%)	⬆️
pymc3/backends/base.py	87.30% <100.00%> (+0.04%)	⬆️
pymc3/backends/sqlite.py	93.54% <100.00%> (+0.03%)	⬆️
pymc3/blocking.py	69.23% <100.00%> (+0.29%)	⬆️
pymc3/distributions/posterior_predictive.py	89.29% <100.00%> (ø)
pymc3/model.py	89.21% <100.00%> (+1.28%)	⬆️
pymc3/step_methods/arraystep.py	93.66% <100.00%> (+0.04%)	⬆️
pymc3/tests/sampler_fixtures.py	96.77% <100.00%> (+0.02%)	⬆️
... and 9 more

[twiecki]

Love the new print output!

Why can't we overload __str__ and continue to use str() instead of a creating a new function?

[ColCarroll]

Looks good to me -- as you said, touches a lot of code, so it'll be good to have it on master and collect bug reports for a while.

@twiecki, I think the problem with just using str everywhere is that this function also handles theano tensors (but I could be wrong)?

[Spaak]

@twiecki:

Why can't we overload __str__ and continue to use str() instead of a creating a new function?

I think in principle it would be possible to keep using str everywhere, but this would mean that in many places the 'name' of the variable would include the distribution details, i.e. before this PR, str(mu) == 'mu' (the default Theano behaviour); after the PR, str(mu) == 'mu ~ Normal(mu=1.0, sigma=0.0)'. I'd say we definitely want to keep referring to variables by just their name. While we can overload __str__ (which this PR overrides), this does not pass through to str, which cannot accept any extra arguments (i.e. str has a fixed signature). It seems to me the only option here is to add the new function. (It also makes sense semantically to me, str(x) gives an informative representation, if we're specifically after a variable's name, use get_var_name(x).)

[Spaak]

Anyone interested in pulling the trigger here? ;) @twiecki @ColCarroll

[twiecki]

Thanks @Spaak!