Estimating bird and bat fatalities caused by wind-turbine facilities is challenging when carcasses are rare and produce counts that are either exactly or very near zero. The rarity of found carcasses is exacerbated when live members of a particular species are rare and when carcasses degrade quickly, are removed by scavengers, or are not detected by observers. With few observed carcass counts, common statistical methods like logistic, Poisson, or negative binomial regression are unreliable (statistically biased) and often fail to provide answers (i.e., fail to converge). Here, we propose a binomial N-mixture model that estimates fatality rates as well as the total number of carcasses when rates are expanded. Our model extends the “evidence of absence” model by relating carcass deposition rates to study covariates and by incorporating terms that naturally scale counts from facilities of different sizes. Our model, which we call Evidence of Absence Regression (EoAR), can estimate the total number of birds or bats killed at a single wind energy facility or a fleet of wind energy facilities based on covariate values. Furthermore, with accurate prior distributions the model's results are extremely robust to sparse data and unobserved combinations of covariate values. In this paper, we describe the model, show its low bias and high precision via computer simulation, and apply it to bat carcass counts observed at 21 wind energy facilities in Iowa.

中文翻译：

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缺失回归的证据：用于估计风能设施死亡人数的二项式 N 混合模型

当尸体稀有并且产生的数量恰好或非常接近于零时，估计由风力涡轮机设施造成的鸟类和蝙蝠死亡是一项挑战。当特定物种的活体成员很少且尸体迅速降解、被清道夫清除或没有被观察者发现时，发现尸体的稀有性会加剧。由于观察到的胴体数量很少，逻辑、泊松或负二项式回归等常用统计方法不可靠（统计偏差），并且通常无法提供答案（即无法收敛）。在这里，我们提出了一个二项式 N 混合模型，该模型估计死亡率以及当比率扩大时的屠体总数。我们的模型通过将胴体沉积率与研究协变量相关联，并通过结合从不同规模的设施中自然缩放计数的术语，扩展了“缺席证据”模型。我们的模型，我们称之为缺失回归证据 (EoAR)，可以根据协变量值估计在单个风能设施或风能设施舰队中杀死的鸟类或蝙蝠的总数。此外，通过准确的先验分布，该模型的结果对于稀疏数据和未观察到的协变量值组合非常稳健。在本文中，我们描述了该模型，通过计算机模拟展示了其低偏差和高精度，并将其应用于爱荷华州 21 个风能设施中观察到的蝙蝠尸体计数。我们称之为缺失回归的证据 (EoAR)，可以根据协变量值估计在单个风能设施或风能设施舰队中杀死的鸟类或蝙蝠的总数。此外，通过准确的先验分布，该模型的结果对于稀疏数据和未观察到的协变量值组合非常稳健。在本文中，我们描述了该模型，通过计算机模拟展示了其低偏差和高精度，并将其应用于爱荷华州 21 个风能设施中观察到的蝙蝠尸体计数。我们称之为缺失回归的证据 (EoAR)，可以根据协变量值估计在单个风能设施或风能设施舰队中杀死的鸟类或蝙蝠的总数。此外，通过准确的先验分布，该模型的结果对于稀疏数据和未观察到的协变量值组合非常稳健。在本文中，我们描述了该模型，通过计算机模拟展示了其低偏差和高精度，并将其应用于爱荷华州 21 个风能设施中观察到的蝙蝠尸体计数。