It’s a bit difficult to diagnose as we dont know what is the function of reducedOp, but looking at the posterior plot there are a lot of weight concentrated around 0 for sigma. I would start with using a more informative prior, and change HalfCauchy to HalfNormal:
tau = pm.HalfNormal('tau', sd=2.5)
...
sigma = pm.HalfNormal('sigma', sd=2.5, shape=Ns*(Ne-1))