Thank you for the insight ! I tried as you suggested. For a setup with lam = 3 and p = 0.3, I tried using a Beta prior on p with some fairly extreme ( I believe ) prior knowledge baked in – I set alpha = 24 and beta = 56, such that the mean of the prior on p was at exactly 0.3. That looks like this :
Unfortunately, this still doesn’t work :
Any other thoughts very much appreciated.