AI 中文总结
针对多调查协议干扰下的种群丰度估计，提出两阶段估计框架，将样本损失校准与检测概率估计分离，推导稳健方差估计器，模拟显示比贝叶斯层次联合模型能更可靠地量化不确定性，并通过实例说明其实用性。
AI 中文摘要
从实地调查估计种群丰度通常因多种调查协议之间的干扰而变得复杂。本文针对检测过程相互作用的丰度模型提出了一个两阶段估计框架，这种相互作用会导致漏检和因调查程序造成的样本损失。我们的方法将样本损失的校准与检测概率的估计分开，避免了完全联合层次模型中可能出现的反馈和弱可识别性问题。我们还推导了一种三明治型稳健方差估计器，将第一阶段的不确定性传播到第二阶段，并且在某些模型误设形式下仍然有效。模拟研究表明，该方法比贝叶斯层次联合模型能提供更可靠的不确定性量化，后者即使在正确设定下也往往低估不确定性。我们用来自入侵性赤腹松鼠的体外寄生虫丰度数据说明了该方法的实际效用。
英文摘要
Estimating population abundance from field surveys is often complicated by interference between multiple survey protocols. In this paper, we propose a two-stage estimation framework for abundance models in which detection processes interact, leading to both missed detections and sample loss caused by survey procedures. Our approach separates the calibration of sample loss from the estimation of detection probability, thereby avoiding the feedback and weak identifiability that can arise in fully joint hierarchical models. We further derive a sandwich-type robust variance estimator that propagates first-stage uncertainty into the second stage and remains valid under certain forms of model misspecification. Simulation studies demonstrated that the proposed method provides more reliable uncertainty quantification than a Bayesian hierarchical joint model, which tends to underestimate uncertainty even under correct specification. We illustrate the practical utility of the method using ectoparasite abundance data from the invasive Pallas's squirrel \textit{Callosciurus erythraeus}.
