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In this example from PyMC3 (https://docs.pymc.io/notebooks/GLM-hierarchical.html) there is estimation of posterior distribution with 1 dimensional sample (samples from dataset have only one feature). 

    # Hyperpriors for group nodes
    mu_a = pm.Normal('mu_a', mu=0., sigma=100)
    sigma_a = pm.HalfNormal('sigma_a', 5.)
    mu_b = pm.Normal('mu_b', mu=0., sigma=100)
    sigma_b = pm.HalfNormal('sigma_b', 5.)

    # Intercept for each county, distributed around group mean mu_a
    # Above we just set mu and sd to a fixed value while here we
    # plug in a common group distribution for all a and b (which are
    # vectors of length n_counties).
    a = pm.Normal('a', mu=mu_a, sigma=sigma_a, shape=n_counties)
    # Intercept for each county, distributed around group mean mu_a
    b = pm.Normal('b', mu=mu_b, sigma=sigma_b, shape=n_counties)

    # Model error
    eps = pm.HalfCauchy('eps', 5.)

    radon_est = a[county_idx] + b[county_idx]*data.floor.values

    # Data likelihood
    radon_like = pm.Normal('radon_like', mu=radon_est,
                           sigma=eps, observed=data.log_radon)

How to generalize if my dataset samples had N-dimensional feature? I've tried to implement inner product with

radon_est = a[county_idx] + np.dot(b[county_idx],data)

but it doesn't work

Lorenzo Vannucchi
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  • Try `b = pm.MvNormal(...` instead of `Normal`? https://docs.pymc.io/api/distributions/multivariate.html#pymc3.distributions.multivariate.MvNormal – shadowtalker May 19 '20 at 16:17
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    Alternatively try `GLM.from_formula` as demonstrated in this example: https://docs.pymc.io/notebooks/GLM.html#Hierarchical-GLM – shadowtalker May 19 '20 at 16:18

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