Estimating Abundance from Presence–Absence Maps via a Paired Negative‐Binomial Model
针对从存在-缺失数据估计丰度的难题，提出基于配对负二项模型的一致且渐近正态的估计量，并扩展为四重负二项模型以解释先前有争议的启发式方法，通过模拟和森林树种数据验证。
Abstract The estimation of abundance from presence–absence data is an intriguing problem in applied statistics. The classical Poisson model makes strong independence and homogeneity assumptions and in practice generally underestimates the true abundance. A controversial ad hoc method based on negative‐binomial counts (Am. Nat.) has been empirically successful but lacks theoretical justification. We first present an alternative estimator of abundance based on a paired negative binomial model that is consistent and asymptotically normally distributed. A quadruple negative binomial extension is also developed, which yields the previous ad hoc approach and resolves the controversy in the literature. We examine the performance of the estimators in a simulation study and estimate the abundance of 44 tree species in a permanent forest plot.