Dear Stan community,
we just published a preprint on hidden Markov/Kalman filter models for the inference of the hidden chemical reaction network of Ion channels. The Kalman filter is a stochastic approximation to the chemical Master equation (CME) and we benchmark it against the deterministic approach of Rate equations in the model training and selection situation. The classical hidden Markov approach is computationally not feasible due the complexity in the number of molecules. Therefore we wanted an approximation to the stochastic dynamics which is better then assuming everything behaves just as the mean value (deterministic Rate equations). While the propensities are linear the difficulties arise from low dimensional observation space compared to the possibly high dimensional protein dynamics and that few is known a priori about the model topology.
We test, continuous model expansion, WAIC, AIC Bayesian cross validation, Maximum a Posteriori crossvalidation and a non Bayesian second Moment Based Model selection strategy on one and two dimensional time series data. We observe various advantages compared to deterministic modeling.
At the core of model we used the single molecule first order Markov dynamics to derive a state depended process noise model.
Additionally, we were able to derive approximate filtering equations for measurement noise which depends on the hidden state which is not the usual Kalman filter context.
I hope you like reading it. And I am happy to take your comments
The next research steps will be to apply the algorithm to real data and to play around with better priors.
Are there any recommendations for weakly informative priors on chemical rates in particular when there is not just a lower bound but also an upper bound due to the limited time sampling of the data.
Jan Münch