I’m hoping someone can help me figure out why PyMC3 is converging on a different estimate than (what seems to me to be) the same model written by Kruschke in R and inferred via Gibbs sampling in JAGS.
Here’s a notebook that shows the two models estimating the difference in means from unbalanced groups.
The different inferences seem come from the SD parameter in the prior for the groups’ means. Kruschke’s BEST defaults to using a tau precision estimate (\sigma^{-2}) based on the SD of the observed data, specifically (5\sigma)^{-2}. When I use the same, the sharply peaked prior pulls the estimated means together and reduces the estimated difference between them. But for some reason that doesn’t happen in JAGS, which correctly estimates both groups’ means using the same prior as PyMC3.
I have no idea why inference based on exactly the same priors and data converges to such different estimates in JAGS and NUTS in PyMC3. Anyone have thoughts?
Thanks for the help!!