Rolling Regression in PyMC

I see. Awesome! One last question out of curiosity: the current model definition is saying that alpha and beta are independent, but in theory is possible to write these as a multivariate normal distribution, i.e.

coords = {
    'regression':windowed_endog.columns,
    'params'=['alpha', 'beta']
}
coefs = pm.MvNormal('coefs', mu=mu, chol=chol, dims=['regression', 'params'])

Overall, this should enable us to provide some more prior information to these parameters. Does this make sense at all even though the columns in the data matrix represent independent regressions?