Gelfand Alan E, Vounatsou Penelope
Department of Statistics, University of Connecticut, Storrs, USA.
Biostatistics. 2003 Jan;4(1):11-25. doi: 10.1093/biostatistics/4.1.11.
In the past decade conditional autoregressive modelling specifications have found considerable application for the analysis of spatial data. Nearly all of this work is done in the univariate case and employs an improper specification. Our contribution here is to move to multivariate conditional autoregressive models and to provide rich, flexible classes which yield proper distributions. Our approach is to introduce spatial autoregression parameters. We first clarify what classes can be developed from the family of Mardia (1988) and contrast with recent work of Kim et al. (2000). We then present a novel parametric linear transformation which provides an extension with attractive interpretation. We propose to employ these models as specifications for second-stage spatial effects in hierarchical models. Two applications are discussed; one for the two-dimensional case modelling spatial patterns of child growth, the other for a four-dimensional situation modelling spatial variation in HLA-B allele frequencies. In each case, full Bayesian inference is carried out using Markov chain Monte Carlo simulation.
在过去十年中，条件自回归建模规范在空间数据分析中得到了广泛应用。几乎所有这些工作都是在单变量情况下完成的，并且采用了不合适的规范。我们在此的贡献是转向多变量条件自回归模型，并提供产生恰当分布的丰富、灵活的类别。我们的方法是引入空间自回归参数。我们首先阐明可以从马尔迪亚（1988）的族中开发出哪些类别，并与金等人（2000）的近期工作进行对比。然后，我们提出一种新颖的参数线性变换，它提供了一种具有吸引人解释的扩展。我们建议将这些模型用作分层模型中第二阶段空间效应的规范。讨论了两个应用；一个用于二维情况，对儿童生长的空间模式进行建模，另一个用于四维情况，对HLA - B等位基因频率的空间变化进行建模。在每种情况下，都使用马尔可夫链蒙特卡罗模拟进行全贝叶斯推断。
