Conducting complete surveys on flora and fauna species within a sampling unit (or quadrat) of interest can be costly, particularly if there are several species in high abundance. A commonly used approach, which aims to reduce time and costs, consists of occurrence data reflecting the status of occupancy of a species– e.g., rather than counting every individual, the survey is stopped as soon as one individual has been observed. Although this approach is cheaper to conduct than a complete survey, some statistical efficiency in model estimators is lost. In this study, we consider occurrence data as a special case of right-censored count data where the collecting process stops until some set threshold on the number of observed individuals is reached. We then propose a new class of regression estimation models for right-censored count data that incorporate information from detection times (or catch effort) collected during sampling. First, we show that incorporating ancillary information in the form of detection times can greatly improve statistical efficiency over, say, right-censored Poisson or negative binomial models. Furthermore, the proposed models retain the same cost-effectiveness as censored-type models. We also consider zero-truncated and zero-inflated models for a variety of count data types. These models can be extended to a more general class of mixed Poisson models. We investigate model performance on simulated data and give two examples consisting of plant abundance data and bat acoustics data. Supplementary materials accompanying this paper appear online.

中文翻译：

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具有检测时间的右删失混合泊松计数模型

对感兴趣的采样单位（或样方）内的动植物物种进行全面调查可能成本很高，尤其是在有多个物种丰度高的情况下。一种旨在减少时间和成本的常用方法包括反映物种占有状态的发生数据——例如，不是计算每个个体，只要观察到一个个体就停止调查。尽管这种方法比完整调查更便宜，但模型估计器的某些统计效率会丢失。在这项研究中，我们将发生数据视为右删失计数数据的一种特殊情况，其中收集过程停止，直到达到观察到的个体数量的某个设定阈值。然后，我们为右删失计数数据提出了一类新的回归估计模型，该模型包含来自采样期间收集的检测时间（或捕获努力）的信息。首先，我们表明以检测时间的形式结合辅助信息可以大大提高统计效率，例如右删失泊松或负二项式模型。此外，所提出的模型保留了与审查型模型相同的成本效益。我们还考虑了各种计数数据类型的零截断和零膨胀模型。这些模型可以扩展到更一般的混合泊松模型类。我们研究了模拟数据的模型性能，并给出了两个由植物丰度数据和蝙蝠声学数据组成的示例。本文随附的补充材料出现在网上。