Inference for Poisson and multinomial models for capture-recapture experiments

Abstract

SUMMARY Capture-recapture models have been formulated both as Poisson and as multinomial distributions. Maximum likelihood estimates of parameters under the two models are compared. For parameters which do not involve the population size the asymptotic covariances are shown to be the same. For certain classes of capture-recapture experiments both Poisson and multinomial models can be used. In the Poisson models (Cormack, 1979) the numbers of observed individuals with different total capture histories w are regarded as independent Poisson variates with means Npf,o N being some measure of the unknown size of the population and p, (0) being specified functions of parameters 0 representing the demography of the population and the behavioural interaction of individuals with the sampling process. In the multinomial models (Darroch, 1958) N individuals are regarded as being multinomially distributed into a number of capture histories, the observable ones with probabilities ph, and the unobservable category with probability l-p*, where p*= Xp' S 1. Sandland & Cormack (1984) explored the relationships between the Poisson and multinomial models and showed that the asymptotic variance of the maximum likelihood estimate of N under the Poisson model is related to that obtained (Fienberg, 1972) under the multinomial model by