If I understand correctly, the iteration in the paper refer to each MCMC draw (using Gibbs sampler) right?
In that case, your problem could be breakdown to 2:
- implement the Stochastic Factor model in PyMC3. I think you are on a right path of reading stochastic vol and rolling regression example, time-varying parameters could be implemented using a
theano.scan, but in many case it could be implemented even without. - Gibbs sampler, this part is a bit more tricky, as you need experience of implementing sampler. But since you are trying to implement a special sampler, you can always extract the logp function from the model, and wrap it in a python control flow to do updates.