Quick Harrison, Banerjee Sudipto, Carlin Bradley P
University of Minnesota.
Ann Appl Stat. 2013;7(1):154-176. doi: 10.1214/12-AOAS600. Epub 2013 Apr 9.
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.
地理信息系统（GIS）的进展导致了近期时空数据库及相关统计建模的大量涌现。在此，我们偏离了时空建模方面颇为丰富的文献，考虑空间离散（例如，区域汇总数据）但时间连续的情形。在这个应用中，我们的主要目标是对加利福尼亚州县级月度哮喘住院率数据集中的时间过程梯度进行推断，同时考虑相邻县之间时间过程的空间相似性。在此使用连续时间模型可实现比数据采样分辨率更高的推断。我们并非采用参数形式对时间进行建模，而是选择在动态马尔可夫随机场框架内嵌入一个更灵活的随机过程。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，从而能够以后验预测的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，此时我们关注在考虑季节性、时空臭氧水平以及几个空间解析的重要社会人口协变量后，残差和拟合率曲线的时间变化。
