Hierarchical model varying indexing of distributions

Questions v5
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5

I think it’s also important to realize this equivalence:

rng = np.random.default_rng(1234)
beta_location_1 = rng.normal()
beta_location_year_1 = rng.normal(loc=beta_location_1, size=n_years)

rng = np.random.default_rng(1234)
beta_location_2 = rng.normal()
beta_year = rng.normal(size=n_years)
beta_location_year_2 = beta_location_2 + beta_year

np.allclose(beta_location_year_1, beta_location_year_2)
>>> Out: True

A model with additive parameters is a hierarchy, just written in a different way. You can compare how I wrote beta_location_year_2 with a non-centered parameterization to see that the years will be clustered at the mean determined by the location, exactly as you describe (just imagine there is a sigma_year hanging out in front of beta_year).

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