In my experience (though I certainly hope that someone does have differing experience from myself, and can tell you some effective best practices), anything larger than ~100 var.s, and ~4000 datapoints is going to kill any hope of even a basic regression in Pymc3.

I attempted once to get a regression such as the above going, and spent a couple of months on it, making sure to A) parametrize all my variables correctly, B) use slightly more informative priors when possible to just make the model run, C) limit my variables from the original 400+ to just the 100 most informative ones in the end, and D) ran everything on a Google Compute cluster, and the regression would *barely* finish after 8+ hr.s each time, and that was the absolute limit.

The numbers you are referencing unfortunately are pure-ML territory, and Bayesian statistics afaik can’t deal with them yet.