随机效应复合泊松模型，用于表示具有额外零值的数据
Random effects compound Poisson model to represent data with extra zeros
摘要：
本文描述了一种用于零膨胀数据建模的基于复合泊松的随机效应结构。在应用统计学的许多领域中，例如在生态学中，当试图建模和预测物种计数（离散数据）或丰度分布（连续数据）时，都会发现大比例的零数据。对这些数据建模的标准方法包括混合模型和两部分条件模型。与这些方法相反，这里提出的随机模型在尺度变化方面表现一致，因为它们在建模步骤中模仿了显着泊松过程的收获。随机效应用于解释不均匀性。在本文中，模型设计和推理都依赖于条件思维来理解各个数量层之间的联系：参数，潜变量，包括随机效应和零膨胀观测。这些简约的层次模型的潜力为零膨胀的数据举例说明使用两个海洋大型无脊椎动物丰度数据集从一个大规模的科学底拖网调查。期望最大化算法与蒙特卡罗步骤的基础上重要性抽样检查此模型结构上的模拟数据集：它被证明是工作良好的参数估计，但参数值的问题时，重新评估的实际覆盖水平的置信区域远离渐近条件。
英文摘要：
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and predict species counts (discrete data) or abundance distributions (continuous data). Standard methods for modeling such data include mixture and two-part conditional models. Conversely to these methods, the stochastic models proposed here behave coherently with regards to a change of scale, since they mimic the harvesting of a marked Poisson process in the modeling steps. Random effects are used to account for inhomogeneity. In this paper, model design and inference both rely on conditional thinking to understand the links between various layers of quantities : parameters, latent variables including random effects and zero-inflated observations. The potential of these parsimonious hierarchical models for zero-inflated data is exemplified using two marine macroinvertebrate abundance datasets from a large scale scientific bottom-trawl survey. The EM algorithm with a Monte Carlo step based on importance sampling is checked for this model structure on a simulated dataset : it proves to work well for parameter estimation but parameter values matter when re-assessing the actual coverage level of the confidence regions far from the asymptotic conditions.
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