I wonder if someone could clarify what P0 really is. For instance, in the example notebooks to pymc-experimental , I found the following statement:

P0_diag = pm.Gamma("P0_diag", alpha=2, beta=5, dims=P0_dims[0])
P0 = pm.Deterministic("P0", pt.diag(P0_diag), dims=P0_dims)

A Gamma distribution is usually used as a prior for a standard deviation, not for a variance. So, does P0 as used above is a covariance matrix or the square-root of a covariance matrix?

Moreover, in structural.py, I frequently find statements like the following for a cycle:

if self.innovations:
sigma_cycle = self.make_and_register_variable(f"sigma_{self.name}", shape=(1,))
self.ssm["state_cov", :, :] = pt.eye(self.k_posdef) * sigma_cycle

So the name "state_cov" suggests that I define a variance, however, the right-hand side suggests that I define a standard deviation (sigma_cycle is the standard deviation of the cycle disturbance).

Any help would be appreciated.