The estimation of the size of a population is, in general, performed using capture–recapture experiments. In this paper, we consider a closed population capture–recapture model in which individuals are captured independently and with the same probability in each sampling occasion, but the probabilities may vary from occasion to occasion. The unknown number of individuals is the parameter of interest, while the capture probabilities are the nuisance ones. Four likelihood functions free of nuisance parameters, namely the profile, conditional, uniform and Jeffrey’s integrated likelihood functions are derived and procedures for point and interval estimation are discussed. The estimation of population size is illustrated on a real dataset. The frequentist properties of the estimators are evaluated by means of a simulation study. The Jeffrey’s integrated likelihood achieved the best performance over all considered estimators for both point and interval estimation, particularly in situations with little information with small number of elements, small capture probabilities and small number of capture occasions.
"Likelihood-based inference for population size in a capture–recapture experiment with varying probabilities from occasion to occasion." Braz. J. Probab. Stat. 30 (1) 47 - 69, February 2016. https://doi.org/10.1214/14-BJPS255