基于过程的空间融合模型与异构空间数据的融合：一个统一框架
Combining Heterogeneous Spatial Datasets with Process-based Spatial Fusion Models: A Unifying Framework
摘要：
在现代空间统计学中，收集的数据结构变得更加异构。根据空间数据的类型，使用不同的空间数据建模策略。例如，用于地质统计数据的克里金方法;用于格点数据的高斯马尔可夫随机场模型;或用于点模式数据的对数高斯Cox过程。尽管有这些不同的建模选择，但潜在的科学数据生成（潜在）过程的性质通常是相同的，可以用一些连续的空间表面来表示。在本文中，我们介绍了一个统一的框架，基于过程的多变量空间融合模型。该框架可以联合分析所有上述三种类型的空间数据（或其任何组合）。此外，该框架可适应地统计数据和格点数据的不同条件分布。我们表明，一些既定的方法，如线性模型coregionalization，可以被视为我们提出的框架的特殊情况。我们使用Stan和INLA在R中提供灵活和可扩展的实现。模拟研究证实，潜在过程的预测性能提高，因为我们从单变量空间模型到多变量空间融合模型。介绍的框架说明使用一个横截面研究与瑞士的国家队列数据集，我们研究呼吸系统疾病和肺癌之间的潜在空间风险模式的差异。
英文摘要：
In modern spatial statistics, the structure of data that is collected has become more heterogeneous. Depending on the type of spatial data, different modeling strategies for spatial data are used. For example, a kriging approach for geostatistical data; a Gaussian Markov random field model for lattice data; or a log Gaussian Cox process for point-pattern data. Despite these different modeling choices, the nature of underlying scientific data-generating (latent) processes is often the same, which can be represented by some continuous spatial surfaces. In this paper, we introduce a unifying framework for process-based multivariate spatial fusion models. The framework can jointly analyze all three aforementioned types of spatial data (or any combinations thereof). Moreover, the framework accommodates different conditional distributions for geostatistical and lattice data. We show that some established approaches, such as linear models of coregionalization, can be viewed as special cases of our proposed framework. We offer flexible and scalable implementations in R using Stan and INLA. Simulation studies confirm that the predictive performance of latent processes improves as we move from univariate spatial models to multivariate spatial fusion models. The introduced framework is illustrated using a cross-sectional study linked with a national cohort dataset in Switzerland, we examine differences in underlying spatial risk patterns between respiratory disease and lung cancer.
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