Jin Xiaoping, Banerjee Sudipto, Carlin Bradley P
University of Minnesota, Minneapolis, USA.
J R Stat Soc Series B Stat Methodol. 2007 Nov 1;69(5):817-838. doi: 10.1111/j.1467-9868.2007.00612.x.
With the ready availability of spatial databases and geographical information system software, statisticians are increasingly encountering multivariate modelling settings featuring associations of more than one type: spatial associations between data locations and associations between the variables within the locations. Although flexible modelling of multivariate point-referenced data has recently been addressed by using a linear model of co-regionalization, existing methods for multivariate areal data typically suffer from unnecessary restrictions on the covariance structure or undesirable dependence on the conditioning order of the variables. We propose a class of Bayesian hierarchical models for multivariate areal data that avoids these restrictions, permitting flexible and order-free modelling of correlations both between variables and across areal units. Our framework encompasses a rich class of multivariate conditionally autoregressive models that are computationally feasible via modern Markov chain Monte Carlo methods. We illustrate the strengths of our approach over existing models by using simulation studies and also offer a real data application involving annual lung, larynx and oesophageal cancer death-rates in Minnesota counties between 1990 and 2000.
随着空间数据库和地理信息系统软件的随时可用,统计学家越来越多地遇到具有多种关联类型的多元建模设置:数据位置之间的空间关联以及位置内变量之间的关联。尽管最近通过使用协同区域化线性模型解决了多元点参考数据的灵活建模问题,但现有的多元面元数据方法通常存在对协方差结构的不必要限制或对变量条件顺序的不良依赖。我们提出了一类用于多元面元数据的贝叶斯层次模型,该模型避免了这些限制,允许对变量之间以及区域单元之间的相关性进行灵活且无顺序的建模。我们的框架包含了一类丰富的多元条件自回归模型,通过现代马尔可夫链蒙特卡罗方法在计算上是可行的。我们通过模拟研究说明了我们的方法相对于现有模型的优势,并提供了一个涉及1990年至2000年明尼苏达州县年度肺癌、喉癌和食管癌死亡率的实际数据应用。