Let’s say we need to use 1 regression equation (Linear regression) and 1 classification (probit classification). Is it possible to correlated errors of these 2 different models. I was thinking on a multivariate normal, but it might not be the best idea.

This WIP notebook may give you other ideas: Bayesian copula estimation example notebook by drbenvincent · Pull Request #257 · pymc-devs/pymc-examples · GitHub

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Without commenting on the method itself, nothing stops you from stacking the means of two GLMs, adding a covariance matrix, and estimating them jointly as a Multivariate Normal. Seems like in the worst case you will just get a diagonal covariance matrix (ok ok the real worst case is infinity divergences)

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