Correlation in Posterior for Slope Parameters (categorical)

Questions
4

Hello @dilsher_dhillon :slight_smile:

thank you very much for you answer, it is very reassuring!
Just a couple of addtional points:

  1. Asserting that the posterior for the levels of a categorical predictor overlaps isn’t a synonynm of correlation?

  2. I know categorical variables are indicized in PyMC3, the reason I call \beta_{j} a slope is that in my mind I see the linear model as a one-hot encode so \mu_{i} \sim \alpha + 1\beta_{ij} (also I am putting an effort to think at ANOVAs more in terms of linear models as it seems to make things easier :rofl:)

  3. I have ran more complicated models with more data in a fraction of the time of the linear model specified above. I know NUTS tend to slow down considerably if parameters’ posteriors are correlated.

My suspect was that since, as you said, the posterior for the groups overlap (i.e. they appear perfectly correlated to the sampler) NUTS was having an hard time doing its job.