Are orphen nodes in a theanos computational graph a problem?

Questions
1

Hi Pymc3 Community,
I often use tt.set_tensor to fix values in a matrix of parameters, for example:

params = pm.Normal('params', mu=0, sd=1, shape=(3,3))
for i in range(3):
   params = tt.set_tensor(params[i,i], 0)

Now the diagnonal elements of params are “orphened” (sorry i know thats not the right word) and never connect to an observed variable. They will just sample from the prior. I’ve always assumed this is not an issue, but I wonder if there is a better way.
Another 2 ways i can think of are:

  1. Create a (3,2) shape of normals, and then place them in the off diagonals of params:
real_params = pm.Normal('params', mu=0, sd=1, shape=(3,2))
params = tt.zeros((3,3))
for i in range(3):
    for j in range(2):
            if i <= j:
                j_param = j + 1
            else:
                j_param = j
         params = tt.set_tensor(params[i,j_param], real_params[i,j])
  1. Create a (3,3) set of normals, but place a very strong and very small prior on the sd of the diagnonal elements:
params = pm.Normal('params', mu=0, sd=[[0.00001,1,1],[1,0.00001,1],[1,1,0.00001]], shape=(3,3))

All of these approaches sample just fine, but which is considered best practice?

2

Usually this shouldnt be an issue, unless you have something that is difficult to sample from (high dimensional, heavy tail, etc).

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