This is a very widely used model among ecologists to estimate number of (unmarked) individuals by repeated counts. By Royle 2003
We implemented a simpler version here, where there are R sites and each site is sampled T repeats, the data y_{it} are counts. The model is there is a latent N_i~Pois(lambda) and y_{it}~Bin(N_i, p) independent, the goal is to estimate p and lambda.