Population size estimation based on the capture-recapture experiment is an interesting problem in various fields including epidemiology, criminology, demography, etc. In many real-life scenarios, there exists inherent heterogeneity among the individuals and dependency between capture and recapture attempts. A novel trivariate Bernoulli model is considered to incorporate these features, and the Bayesian estimation of the model parameters is suggested using data augmentation. Simulation results show robustness under model misspecification and the superiority of the performance of the proposed method over existing competitors. The method is applied to analyse real case studies on epidemiological surveillance. The results provide interesting insight on the heterogeneity and dependence involved in the capture-recapture mechanism. The methodology proposed can assist in effective decision-making and policy formulation.

翻译：基于捕获-再捕获实验的总体规模估计是流行病学、犯罪学、人口学等多个领域中的一个有趣问题。在许多现实场景中，个体间存在固有异质性，且捕获与再捕获尝试之间存在依赖性。为整合这些特征，本文提出了一种新颖的三变量伯努利模型，并通过数据增强方法建议对模型参数进行贝叶斯估计。模拟结果表明，在模型设定错误时该方法具有稳健性，且所提方法的性能优于现有竞争方法。该方法被应用于分析流行病监测中的真实案例研究，结果为捕获-再捕获机制所涉及的异质性与依赖性提供了有趣的见解。所提出的方法论可辅助有效决策与政策制定。