Improve support for statespace post-estimation tasks when working with point estimates #583
Description
Currently, all post-estimation tasks in statespace assume we have access to a full posterior. Rather than working with the mean/covariance of the KF, we use each parameterization in the posterior to get a single realization from that particular filter, then report the collection over all the draws.
When we have lots of parameters, this works fine. But when you fit a model via MAP, it gives unexpected results. For example, here is the forecast of a VAR(2) model using MAP:
The forecast (in green) has random noise, and will not be deterministic -- if I run ss_mod.forcast(map_result) again, I get a new forecast. The same will be true for the sample_conditional_posterior, impulse_response_function, etc.
It would be good if we have a mode that works directly with the mean/covariance implied by a single filter parameterization, and allow users to request that. We should also switch to that mode automatically if we see that there is only one set of parameters being passing in (chains=1, draws=1, or no chain/draw dims).