Bayesian Filtering

Here is the problem -- there is an open state (O) and closed state (C) and a stuck (inactivated) state (S). Transitions between these states happen like this

$O \rightleftharpoons C \rightleftharpoons S$

Transitions between O and S never happen (i.e. the probability is negligible) without C being an intermediary state. The observed current is zero in C and S and one in O. And there is noise. We want to estimate the probability of transitioning back and forth between C and S, P_cs, and P_sc. Let's say we know everything else (i.e. the probabilities of transitioning back and forth between open and closed states).

Here is what some data might look like:

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