模拟加州哮喘住院数据的时间梯度
Modeling temporal gradients in regionally aggregated California asthma hospitalization data
摘要：
地理信息系统（GIS）的进步导致了时空数据库和相关统计建模的巨大发展。在这里，我们通过考虑空间离散的设置（例如，区域汇总数据），但时间是连续的。我们在这个应用程序中的主要目标是进行推理的时间过程的梯度在我们的数据集每月县级哮喘住院率在加利福尼亚州，而在同一时间占相邻县的时间过程的空间相似性。这里使用连续时间模型允许以比数据采样更精细的分辨率进行推断。而不是使用参数形式来建模时间，我们选择了一个更灵活的随机过程嵌入在一个动态马尔可夫随机场框架。通过矩阵值协方差函数，我们可以确保时间过程实现是均方可微的，并且因此可以以后验预测方式对时间梯度进行推断。我们使用这种方法来评估时间梯度，我们关心的是占季节性，时空臭氧水平和几个空间分辨的重要社会人口协变量后，在残差和拟合率曲线的时间变化。
英文摘要：
Advances in Geographical Information Systems (GIS) have led to the enormous recent burgeoning of spatial-temporal databases and associated statistical modeling. Here we depart from the rather rich literature in space-time modeling by considering the setting where space is discrete (e.g., aggregated data over regions), but time is continuous. Our major objective in this application is to carry out inference on gradients of a temporal process in our data set of monthly county level asthma hospitalization rates in the state of California, while at the same time accounting for spatial similarities of the temporal process across neighboring counties. Use of continuous time models here allows inference at a finer resolution than at which the data are sampled. Rather than use parametric forms to model time, we opt for a more flexible stochastic process embedded within a dynamic Markov random field framework. Through the matrix-valued covariance function we can ensure that the temporal process realizations are mean square differentiable, and may thus carry out inference on temporal gradients in a posterior predictive fashion. We use this approach to evaluate temporal gradients where we are concerned with temporal changes in the residual and fitted rate curves after accounting for seasonality, spatiotemporal ozone levels and several spatially-resolved important sociodemographic covariates.
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