Bug in fast sample posterior predictive?

Questions
6

Let me see if I can be more helpful:

First, On the deterministic / random variable distinction. What I meant to say is that there is no (statistical) link from a deterministic child to its parent rv. That’s why changing d2 did not change neither n2 nor d3. This is to say that in the following model:

with pm.Model() as m:
  x = pm.normal('x')
  y1 = pm.Deterministic('y1', x)
  y2 = pm.Deterministic('y1', x+100)

Adding 100 to y2 will not do anything to either x or y1 (in either prior_predictive, normal sampling or posterior_predictive). I am emphasizing this, because I think it is a separate issue from the ppc question.

Second,

PPC resamples the variables that are missing in the provided trace, conditioned on the values of the parent variables or on the prior if it’s a top level rv. Under normal circumstances it only looks for observed variables as that is it’s main intended behavior, and resamples them given the trace points and the likelihood distribution.

Now, when you specify you want variables other than observed ones it behaves a bit funky. If these exist in the trace, the values are simply copied. If they don’t exist, then it samples them, conditioning on the trace values or the prior (if they are a top level rv):

 with pm.Model() as m: 
    x1 = pm.Normal('x1', 0, 1) 
    x2 = pm.Normal('x2', x1 + 50, 1) 

with m: 
    trace = pm.sample() 

with m: 
    ppc = pm.sample_posterior_predictive(trace)
ppc  # {} empty dictionary

with m: 
     ppc = pm.sample_posterior_predictive(trace, var_names=['x2'])
(ppc['x2'] == trace['x2']).mean()  # 1.0  same values as in the trace

# Now we add a new variable
with m: 
     x3 = pm.Normal('x3', x1 - 50, 1) 

with m: 
     ppc = pm.sample_posterior_predictive(trace, var_names=['x3'])                                                             
ppc['x3'].mean()  # -50.0173504935316

# And run it again
with m: 
     ppc = pm.sample_posterior_predictive(trace, var_names=['x3']) 
ppc['x3'].mean()  # -50.00807725408419  The values change