It sounds like you’re doing online updating; you want to run your filter on incoming streaming data, one point at a time. Is that right? If so, the
statespacemodule won’t help.
Yes, that is exactly right. I have an IOT device that reports data once every minute or so. I need to make continuous guesses on its state, one point at a time.
Do you also want to update the parameter priors whenever new data comes in, or do you only want to update the hidden states?
I expect that, during simulation time, nothing except the hidden state can change in any meaningful way. So I’m fine with a constant initial guess for parameters. The only effect I would like to model is the change in the hidden variables, both due to its intrinsic evolution, and due to changes in observables.
You will need to either use a different distribution or do some kind of transformation (as you bring up in the edit)
Do you have any suggestions on how to proceed?
- It seems that domain reparameterization would disbehave if a state is at the boundary. Is there a way around that?
- Do you have a distribution in mind, that would intrinsically model such boundary conditions? Naively, I would consider using 2 binomial distributions with high enough sample number, for parameter sets (p1,p2) and (p3,p4). But then I also need to stitch them together somehow, because the most important part of this model is to have a dense 4x4 covariance matrix between all parameters. Do you have some suggestions maybe?
- Sorry for being annoying. Is it not possible to have a truncated multivariate normal distribution? There is an univariate distribution like that already. Or is it conceptually impossible somehow.
Thanks a lot for all the help