对Poisson随机变量集合的依赖性
Dependence on a collection of Poisson random variables
摘要：
我们提出了两种新的方法，通过使用潜变量的三层分层模型中的泊松计数之间的依赖关系。感兴趣的随机变量的边缘分布是严格平稳性作为特殊情况的泊松分布。顺序- $p$依赖性详细描述了随机变量的时间序列，然而空间或时空依赖性也是可能的。一个完整的贝叶斯推断的模型和性能的模型说明了在墨西哥的孕产妇死亡率的数值分析。扩展，以应付过度分散也进行了讨论。
英文摘要：
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, however spatial or spatio-temporal dependencies are also possible. 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 cope with overdispersion are also discussed.
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