add potentials to priors when running abc

[aloctavodia]

Because potentials are applied to the likelihood term they are invisible to ABC models. This change it (only for ABC).
Sampling from the prior still is still unaware of potentials, this not fix that as it should be solved in the sampling_prior_predictive function. Unless we decide not to provide a general solution (in that case I will solve it for SMC and SMC/ABC)

[codecov]

Codecov Report

Merging #4016 into master will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##           master    #4016   +/-   ##
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  Coverage   86.77%   86.77%           
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  Files          88       88           
  Lines       14137    14144    +7     
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+ Hits        12267    12274    +7     
  Misses       1870     1870           

Impacted Files	Coverage Δ
pymc3/smc/sample_smc.py	87.95% <100.00%> (+0.45%)	⬆️
pymc3/smc/smc.py	99.49% <100.00%> (+0.01%)	⬆️
pymc3/gp/cov.py	97.96% <0.00%> (ø)

[AlexAndorra]

Thanks @aloctavodia, LGTM! I also added @junpenglao and @lucianopaz as reviewers, as I think they know the context around this better than me.

[lucianopaz]

I'm a bit confused. Why doesn't model.logpt work? To me, it looks like the only difference is that the observed_RVs aren't included in your factors whereas they are in the model.logpt.

[aloctavodia]

SMC needs to evaluate the prior and likelihood terms idenpendently, the sampler progressively turns on the likelihood term. Additionally in ABC, there is no true likelihood. The likelihood is approximated as a discrepancy between observed and simulated data. That's why I am moving the potential to the prior, only for this type of model/sampler

[junpenglao]

This works fine for Potential as a constrain to the prior, but not if the Potential is part of the likelihood term (those you need to add to the likelihood func). Unless there is a way to detect the dependency and add the potential to different term, this change is not safe/correct.

The model that would be incorrect is something like:

with pm.Model() as SMABC_potential_liklihood:
    a = pm.Normal("a", mu=0, sigma=1)
    b = pm.HalfNormal("b", sigma=1)
    c = pm.Potential("c", pm.math.switch(a > 0, 0, -np.inf))  # <== this should be added to prior
    s = pm.Simulator(
        "s", normal_sim, params=(a, b), sum_stat="sort", epsilon=1, observed=data
    )
    pm.Potential("s_p", pm.Normal.dist().logp(s))  # <== this should be added to likelihood

[aloctavodia]

This change only affects SMC-ABC, i.e. models without a likelihood.

[junpenglao]

This change only affects SMC-ABC, i.e. models without a likelihood.

Could you add a warning if there are Potentials in the model to indicate that they will be added to the prior? I dont think it is a common use case for user to write down model like the one I wrote above, but currently we dont forbid ppl to write those kind of model so we might as well raise a warning.

[twiecki]

Thanks @aloctavodia!