Ok, thanks! So it sounds to me that you need both MCMC to estimate the uncertainty in your parameters’ posterior, as well as posterior predictive sampling to check the generative accuracy of your model.
pi and T would be parameters here, and thus would need priors.
I don’t see a big problem here: you’re using the observed kwarg as expected. Note though that it seems you’re not inferring means, cov and var*. Again, I would also use much more informative priors than Uniforms.
In case that helps, here are examples of GP regression using PyMC3 (start at Code 14.30) – this is a port of Statistical Rethinking 2, chapter 14