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:
- 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])
- 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?