A Reparametrization Approach for Dynamic Space-Time Models
A Reparametrization Approach for Dynamic Space-Time Models
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DOI：
10.1080/15598608.2008.10411856
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发表时间：
2008-01-01
影响因子：
0.6
通讯作者：
Ghosh, Sujit K.
中科院分区：
文献类型：
--
作者：
Lee, Hyeyoung;Ghosh, Sujit K.
环境和健康科学等不同领域的研究人员越来越多地使用跨空间和时间收集的数据。在实践中通常使用的时空过程通常是复杂的，因为跨空间和时间的自相关结构是非平凡的，通常是不可分离的，并且在空间和时间上是非平稳的。此外，这种数据集在空间和时间上的维度可能非常大，由于数值不稳定性而导致计算困难。因此，时空建模是一项具有挑战性的任务，特别是基于复杂模型的参数估计由于维数灾难而可能存在问题。我们提出了一种新的重新参数化方法来适应动态时空模型，它允许使用一个非常一般的形式的空间协方差函数。我们的建模贡献是提出一个无约束的重新参数化方法的协方差函数的动态时空模型。所提出的无约束重新参数化方法的一个主要好处是，我们能够实现一个非常高维的协方差矩阵，自动保持正定约束的建模。我们证明了我们提出的重新参数化的动态时空模型的总硝酸盐浓度的大数据集的适用性。
Researchers in diverse areas such as environmental and health sciences are increasingly working with data collected across space and time. The space-time processes that are generally used in practice are often complicated in the sense that the auto-dependence structure across space and time is non-trivial, often non-separable and non-stationary in space and time. Moreover, the dimension of such data sets across both space and time can be very large leading to computational difficulties due to numerical instabilities. Hence, space-time modeling is a challenging task and in particular parameter estimation based on complex models can be problematic due to the curse of dimensionality. We propose a novel reparametrization approach to fit dynamic space-time models which allows the use of a very general form for the spatial covariance function. Our modeling contribution is to present an unconstrained reparametrization method for a covariance function within dynamic space-time models. A major benefit of the proposed unconstrained reparametrization method is that we are able to implement the modeling of a very high dimensional covariance matrix that automatically maintains the positive definiteness constraint. We demonstrate the applicability of our proposed reparametrized dynamic space-time models for a large data set of total nitrate concentrations.