Compound/Gibbs step and discrete suppot

[rrkarim]

• Add tests
• Add Gibbs
• Check on the performance for the one_step in compound sampler
• Improve user design. First, make sampler_type the default for the model with discrete and continuous distributions.
• Add logging as in pymc3
• Fix seed
• Fix the bug with merge of proposal funcs

[rrkarim]

Here is the trivial example from sampling from pm.Categorical:

@pm.model
def categorical():
    var1 = yield pm.Categorical("var1", probs=[0.2, 0.4, 0.4])
    var1 = yield pm.Categorical("var2", probs=[0.1, 0.3, 0.2, 0.2, 0.2])
    var1 = yield pm.Categorical("var3", probs=[0.1, 0.1, 0.1, 0.1, 0.1, 0.5])
trace = pm.sample(categorical(), sampler_type="compound") 
# after the review default attribute should be compound and if there is no
# discrete variable in the model, we choose nuts as the sampler

I've included the notebook with discrete distributions: discrete_distributions_sampling.ipynb

[rrkarim]

Som results with different proposal generations for Poisson. I'm note sure about the poisson proposal generation though. Now it will be able to discover proper samples when scale is provided.

@pm.model
def model():
    var1 = yield pm.Poisson("var1", 4) # gaussian with round dist proposal
    var1 = yield pm.Poisson("var2", 4) # poisson dist proposal
    var2 = yield pm.Poisson("var3", 4) # continous space

trace = pm.sample(model(), 
                  sampler_type="compound", 
                  sampler_methods=[
                      ("var1", RandomWalkM, {"new_state_fn": gaussian_round_fn}),
                      ("var2", RandomWalkM, {"new_state_fn": functools.partial(poisson_fn, scale=4)}), # not sure if this is the right way to define proposal
                  ],
                  trace_discrete=["var1", "var2"])

[rrkarim]

@junpenglao Can you also suggest something better with the trace_discrete argument I've added to sample(). I don't like any additional argument, but it is the only way I can have discreteness in the plot for Poisson (see the Picture above). (tfd.Poisson can sample dtype tf.float32 points only, so delta should also be the same dtype)

[junpenglao]

@rrkarim is this ready for review? if so could you resolve the conflicts?

[junpenglao]

This is awesome contribution! Thanks and great job :-)