Serially correlation binomial data with random cluster sizes occur frequently in environmental and health studies. Such data series have traditionally been analyzed using binomial state-space or hidden Markov models without appropriately accounting for the randomness in the cluster sizes. To characterize correlation and extra-variation arising from the random cluster sizes properly, we introduce a joint Poisson state-space modelling approach to analysis of binomial series with random cluster sizes. This approach enables us to model the marginal counts and binomial proportions simultaneously. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors. This estimation method is computationally efficient and robust since it depends only on the first- and second- moment assumptions of unobserved random effects. Our proposed approach is illustrated with analysis of birth delivery data.

中文翻译：

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一种用于分析具有随机簇大小的二项式级数的联合泊松状态空间建模方法

具有随机簇大小的序列相关二项式数据在环境和健康研究中经常出现。此类数据系列传统上是使用二项式状态空间或隐马尔可夫模型进行分析的，而没有适当考虑集群大小的随机性。为了正确描述随机簇大小引起的相关性和额外变化，我们引入了一种联合泊松状态空间建模方法来分析具有随机簇大小的二项式序列。这种方法使我们能够同时对边际计数和二项式比例进行建模。使用正统的最佳线性无偏预测器开发了我们模型的最佳估计。这种估计方法计算效率高且稳健，因为它仅依赖于未观察到的随机效应的一阶和二阶假设。我们提出的方法通过分析分娩数据来说明。