For comparison, here are the same four posterior probability plots for each of aug1 ... aug4 ran individually through the Mt model in the Stan repository:
I see that it’s not doing that much better. Then I tried to change my simulation to keep the same detection probability for all observations. Then the results are much better:
Again, targets here were 600, 800, 350 & 450. This looks great!
That leads me to suspect that maybe there’s a bug in the implementation of Mt in the Stan repository, or – & maybe this is more likely – it’s just that much harder to infer population size from capture-recapture data with variable detection probability. What do you think?