Vectorization for multi-dimensional hyper-prior

Questions
1

Hello, Have a question when to have a multi-dimensional hyper prior.

Let’s say \mu \in \mathbb{R}^{K \times C}
and \mu_{k,c} \sim N(0,1) for k=1...K and c=1...C.

\beta_{k,c,w}\sim N(\mu_{k,c},1) for w =1,...,W.

In this case, I can do

model2=pm.Model()
with model2:
    mu=pm.Normal('mu',mu=0,sigma=1,shape=(n_K,n_C))
    beta_probs=[]
    for w in range(n_W):
        _beta=pm.Normal("beta_%i" %w,mu=mu,sigma=1,shape=(n_K,n_C))
        beta_probs.append(_beta)
    beta=pm.Deterministic("beta",tt.stack(beta_probs,axis=2))

But, is there any way to vectorize it? such as… (below is not working)

model1=pm.Model()
with model1:
    mu=pm.Normal('mu',mu=0,sigma=1,shape=(n_K,n_C))
    beta=pm.Normal('beta',mu=mu,sigma=1,shape=(n_K,n_C,n_W))

Thanks a lot for the help…

2

You can either do:

with model1:
    mu=pm.Normal('mu',mu=0,sigma=1,shape=(n_K,n_C))
    beta=pm.Normal('beta',mu=mu,sigma=1,shape=(n_W,n_K,n_C))

or

with model1:
    mu=pm.Normal('mu',mu=0,sigma=1,shape=(n_K,n_C))
    beta=pm.Normal('beta',mu=mu[..., None],sigma=1,shape=(n_K,n_C,n_W))
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