1978/12/01 by Frank Louis Carle, Mike R. Strub · 460 citations
Computer Science · Environmental Science · Mathematics · #Applied mathematics #Bayesian Methods and Mixture Models #Census and Population Estimation #Estimation #Estimator #Fish Ecology and Management Studies #Mathematics #Maximum likelihood #Multinomial distribution #Population #Population size #Sample size determination #Statistics
paper · doi:10.2307/2530381
published in Biometrics 34(4), 621 (Oxford University Press)
openalex publication_date 1978/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
Summary The theory leading to the maximum likelihood (ML) estimation of population size from removal data is reviewed. The assumptions of the removal method are that ehanges in population size occur only through eapture, and the probability of eapture is equal for all individuals in a population during the removal sequenee. A modifieation of the multinomial model is proposed and a new estimator developed. In the new model the likelihood density of the probability of capture is weighted with a beta prior. The ease where oe = d = 1 (uniform prior) is eompared with ML estimation andfornd to have lower bias and varianee. The new method, unlike previous methods, does not fail for aS?y eateh veetor thus avoiding the substitution of the total eateh for the estimate of N when infinite7 estimates occur. The assumptions that result from applying large sample theory while estimQting the varianee of ML estimates are reviewed, and a eondition presentedfor the inadequacy of avymptotie varianee formulae when using the weighted estimator (oe = F = 1). Examples illustrating the use of the new method are given, one example illustrates the use of the new method when previous methods fail. Various assumption violations are investigated and the new method is found to be more robust against the violation of assumptions than previous methods.