Hi Jesse,
Thank you for your answer that was very helpful!
To clarify, I want to model “independent” AR(1) equations for latent volatilities with correlated latent errors, hence why I mentioned in my post that each variance only depends on its own lags and not the lags of the other variances, but why the model still is multivariate. Therefore, I think I would need to amend the line for sigma which should be a batch times batch matrix (since the latent errors across equations are allowed to be correlated).
For the nomenclature: point taken! To provide some additional context, I am actually modelling the conditional variances of the structural shocks of a structural vector autoregression, where I recovered the said structural shocks using a predefined identification strategy. Hence why I refer to the errors in the AR(1) equations (the ones generated by pm.Normal.dist(sigma=sigma)) as “latent errors” while the final variable I recover is named “shocks” in reference to the structural shocks, I hope this clarifies!