Mark–recapture sampling schemes are conventional approaches for population size (N) estimation. In this paper, we mainly focus on providing fixed-length confidence interval estimation methodologies for N under a mark–recapture–mark sampling scheme, where, during the resampling phase, non-marked items are marked before they are released back in the population. Using a Monte Carlo method, the interval estimates for N are obtained through a purely sequential procedure with an adaptive stopping rule. Such an adaptive decision criterion enables the user to “learn” with the subsequent marked and newly tagged items. The method is then compared with a recently developed accelerated sequential procedure in terms of coverage probability and expected number of captured items during the resampling stage. To illustrate, we explain how the proposed procedure could be applied to estimate the number of infected COVID-19 individuals in a near-closed population. In addition, we present a numeric application inspired on the problem of estimating the population size of endangered monkeys of the Atlantic forest in Brazil.

Mark-recapture 抽样方案是种群规模 ( N ) 估计的常规方法。在本文中，我们主要关注在标记-重新捕获-标记抽样方案下为 N 提供固定长度的置信区间估计方法，其中，在重采样阶段，未标记的项目在它们被释放回种群之前被标记。使用蒙特卡罗方法，N的区间估计是通过具有自适应停止规则的纯顺序过程获得的。这种自适应决策标准使用户能够“学习”后续标记和新标记的项目。然后将该方法与最近开发的加速顺序程序在重采样阶段的覆盖概率和捕获项目的预期数量方面进行比较。为了说明这一点，我们解释了如何应用提议的程序来估计接近封闭人群中受感染的 COVID-19 个体的数量。此外，我们提出了一个数字应用程序，其灵感来自于估计巴西大西洋森林中濒临灭绝的猴子的种群规模问题。