Small Sample Inference for Two‐Way Capture‐Recapture Experiments
本文回顾广义Waring分布的性质，并将其作为先验与超几何分布结合，构建贝叶斯模型来估计双向捕获-再捕获实验中的总体规模，提出一种新的可信区间，在小样本下覆盖概率优于传统方法。
Summary The properties of the generalised Waring distribution defined on the non‐negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then we turn to the Petersen model for estimating the population size in a two‐way capture‐recapture experiment. We construct a Bayesian model for by combining a Waring prior with the hypergeometric distribution for the number of units caught twice in the experiment. Credible intervals for are obtained using quantiles of the posterior, a generalised Waring distribution. The standard confidence interval for the population size constructed using the asymptotic variance of Petersen estimator and 0.5 logit transformed interval are shown to be special cases of the generalised Waring credible interval. The true coverage of this interval is shown to be bigger than or equal to its nominal converage in small populations, regardless of the capture probabilities. In addition, its length is substantially smaller than that of the 0.5 logit transformed interval. Thus, the proposed generalised Waring credible interval appears to be the best way to quantify the uncertainty of the Petersen estimator for populations size.