Imputation for partially observed random variables with positive support

Questions
1

I’m looking to do imputation of partially observed random variables with positive support. Everything seems to be going fine for distributions that have support on the entire real line, like the normal distribution. Here’s the unobserved case:

import pymc3 as pm
from numpy.ma import masked_values

with pm.Model() as model:
    pm.Normal("unobserved", mu=0., sigma=1, shape=(2,))
    map_estimate = pm.find_MAP()

print(map_estimate)
print(model.test_point)

{'unobserved': array([0., 0.])}
{'unobserved': array([0., 0.])}

And the partially observed case:

import pymc3 as pm
from numpy.ma import masked_values

MASK_VALUE = -999.
observed_values = np.array([1., MASK_VALUE], dtype=float)
with pm.Model() as model:
    pm.Normal("partially_observed", mu=0, sigma=1, observed=masked_values(observed_values, value=MASK_VALUE), shape=(2,))
    map_estimate = pm.find_MAP()
print(map_estimate)
print(model.test_point)

{'partially_observed_missing': array([0.])}
{'partially_observed_missing': array([0.])}

The unobserved gamma distribution case also seems fine:

import pymc3 as pm
from numpy.ma import masked_values

with pm.Model() as model:
    pm.Gamma("unobserved", alpha=3., beta=1/0.1, shape=(2,))
    map_estimate = pm.find_MAP()
print(map_estimate)
print(model.test_point)

{'unobserved_log__': array([-1.60943927, -1.60943927]), 'unobserved': array([0.19999973, 0.19999973])}
{'unobserved_log__': array([-1.2039728, -1.2039728])}

But the partially observed gamma distribution case converges to a point that is outside of the support of the distribution:

import pymc3 as pm
from numpy.ma import masked_values

MASK_VALUE = -999.
observed_values = np.array([1., MASK_VALUE], dtype=float)
with pm.Model() as model:
    pm.Gamma("partially_observed", alpha=3., beta=1/0.1, observed=masked_values(observed_values, value=MASK_VALUE))
    map_estimate = pm.find_MAP()
print(map_estimate)
print(model.test_point)

{'partially_observed_missing': array([-0.7])}
{'partially_observed_missing': array([0.3])}

I think it might be this same issue that is causing variational inference to fail. Any ideas about what the underlying issue is? All help is very much appreciated.

2

It looks like this is due to the fact that support-constrained variables are usually not sampled on their original scale. I reproduced your issue with lognormal and beta-distributed random variates as well. It would be worth opening an issue on the PyMC3 Github for this.