We propose two novel ways of introducing dependence among Poisson counts through the use of latent variables in a three levels hierarchical model. Marginal distributions of the random variables of interest are Poisson with strict stationarity as special case. Order–p dependence is described in detail for a temporal sequence of random variables. A full Bayesian inference of the models is described and performance of the models is illustrated with a numerical analysis of maternal mortality in Mexico. Extensions to seasonal, periodic, spatial or spatio-temporal dependencies, as well as coping with overdispersion, are also discussed.

中文翻译：

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依赖于Poisson随机变量的集合

我们提出了两种新颖的方法，可通过在三级层次模型中使用潜在变量来引入泊松计数之间的依存关系。特殊情况下，感兴趣的随机变量的边际分布是具有严格平稳性的泊松分布。对于随机变量的时间序列，将详细描述order- p依赖性。描述了模型的完整贝叶斯推论，并通过墨西哥产妇死亡率的数值分析说明了模型的性能。还讨论了对季节，周期性，空间或时空依赖性的扩展，以及应对过度分散的问题。