Handle ppe for `nc_parents`(Partial Dependency) and add tests

[rohanbabbar04]

Description

• Calculate priors for partial dependent arguments, just like in the example
• Add tests for hierarchical models partial dependency.

# One such example
cs_data = pd.read_csv('testdata/chemical_shifts_theo_exp.csv')
diff = cs_data.theo - cs_data.exp
cat_encode = pd.Categorical(cs_data['aa'])
idx = cat_encode.codes
coords = {"aa": cat_encode.categories}
with pm.Model(coords=coords) as model:
    # hyper_priors
    a = pm.Normal("a", mu=1, sigma=10)
    z = pm.HalfNormal("z", sigma=10)

    x = pm.Normal("x", mu=a, sigma=10, dims="aa")

    y = pm.Normal("y", mu=x[idx], sigma=z, observed=diff)

target = pz.Normal(mu=40, sigma=7)

prior, new_prior, pymc_string = pz.ppe(model, target)
print(pymc_string)

[aloctavodia]

Just a clarification the problem is when we have partial dependence. Currently a case like

pm.Normal('μ', mu=μ_mu, sigma=μ_sigma, dims="aa")

is properly handle

[rohanbabbar04]

@aloctavodia For the above example which has partial dependency,

Currently the pymc_string which is generated(definitely does not include x) is

with pm.Model() as model:
   a = pm.Normal("a", mu=40.01,sigma=0.17)
   z = pm.HalfNormal("z", sigma=6.99)

Can you tell me what would be the pymc_string(approximate) which will be generated(a, z, x) which satisfies the target distribution?

[rohanbabbar04]

Description

• Calculate priors for partial dependent arguments, just like in the example
• Add tests for hierarchical models partial dependency.

# One such example
cs_data = pd.read_csv('testdata/chemical_shifts_theo_exp.csv')
diff = cs_data.theo - cs_data.exp
cat_encode = pd.Categorical(cs_data['aa'])
idx = cat_encode.codes
coords = {"aa": cat_encode.categories}
with pm.Model(coords=coords) as model:
    # hyper_priors
    a = pm.Normal("a", mu=1, sigma=10)
    z = pm.HalfNormal("z", sigma=10)

    x = pm.Normal("x", mu=a, sigma=10, dims="aa")

    y = pm.Normal("y", mu=x[idx], sigma=z, observed=diff)

target = pz.Normal(mu=40, sigma=7)

prior, new_prior, pymc_string = pz.ppe(model, target)
print(pymc_string)

What would be the appropriate pymc string which will be generated for partial dependency which satisfies the target distribution?

[aloctavodia]

I will need to check this. But I think a proper way to find it out is to fit the model using PyMC (i.e. use pm.sample) and using a sample from target as the observations

[aloctavodia]

Still checking, but I think we should expect a vector with values between ~0.5 and ~1. I would recommend that you try to get the function to work, in the sense it returns something and report back to me the results, so we can both discuss if they make sense.