I have a data set where birds are marked and observed at 2 sites, and there is resighting heterogeneity at both sites, for a total of 4 states (site A and B, high and low observability). I'm struggling a bit with how to model initial state probabilities, since the distribution of newly marked birds between sites is given by study design (thus deterministic), whereas the distribution between observability classes is unknown (thus probabilistic) and may differ between the two sites. In addition, there's a large year-to-year variation in the distribution of marking effort between the two sites.
Any thoughts on how to model this? Perhaps the initial state probs can be modelled with two steps, first the deterministic and then the probabilistic.
Incidentally, the transitions aren't simple either in a case like this!
Morten