Wang Bingling, Banerjee Sudipto, Gupta Rangan
DEPARTMENT OF BIOSTATISTICS, UNIVERSITY OF CALIFORNIA, LOS ANGELES.
DEPARTMENT OF ECONOMICS, UNIVERSITY OF PRETORIA.
Sankhya B (2008). 2021 Nov;83(Suppl 2):395-414. doi: 10.1007/s13571-020-00233-y. Epub 2020 Aug 18.
Spatial process models are being increasingly employed for analyzing data available at geocoded locations. In this article, we build a hierarchical framework with multivariate spatial processes, where the outcomes are "mixed" in the sense that some may be continuous, some binary and others may be counts. The underlying idea is to build a joint model by hierarchically building conditional distributions with different spatial processes embedded in each conditional distribution. The idea is simple and the resulting models can be fitted to multivariate spatial data using straightforward Bayesian computing methods such as Markov chain Monte Carlo methods. Bayesian inference is carried out for parameter estimation and spatial interpolation. The proposed models are illustrated using housing data collected in the Walmer district of Port Elizabeth, South Africa. Inferential interest resides in modeling spatial dependencies of dependent outcomes and associations accounting for independent explanatory variables. Comparisons across different models confirm that the selling price of a house in our data set is relatively better modeled by incorporating spatial processes.
空间过程模型正越来越多地用于分析地理编码位置处可得的数据。在本文中，我们构建了一个具有多变量空间过程的分层框架，其中结果是“混合的”，即有些可能是连续的，有些是二元的，还有些可能是计数型的。其基本思想是通过分层构建条件分布来构建联合模型，每个条件分布中嵌入不同的空间过程。这个想法很简单，并且所得模型可以使用诸如马尔可夫链蒙特卡罗方法等直接的贝叶斯计算方法来拟合多变量空间数据。进行贝叶斯推断以进行参数估计和空间插值。使用在南非伊丽莎白港瓦尔默区收集的住房数据对所提出的模型进行了说明。推断兴趣在于对依赖结果的空间依赖性以及考虑独立解释变量的关联进行建模。不同模型之间的比较证实，通过纳入空间过程，我们数据集中房屋的销售价格能得到相对更好的建模。
