Improving Bayesian Local Spatial Models in Large Datasets
Improving Bayesian Local Spatial Models in Large Datasets
复制标题
改进大型数据集中的贝叶斯局部空间模型
DOI：
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发表时间：
2019
影响因子：
2.4
通讯作者：
M. Genton
中科院分区：
文献类型：
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作者：
Amanda Lenzi;S. Castruccio;H. Rue;M. Genton
在足够小的时空尺度上分辨的环境过程不可避免地表现出非平稳行为。当数据量很大时，这样的过程对建模和计算都是具有挑战性的。局部模型可以应用于域的不相交区域，而不是显式地对全局非平稳性进行建模。这些区域大小的选择取决于偏差-方差权衡;大区域将具有较小的方差和较大的偏差，而小区域将具有较高的方差和较小的偏差。从建模和计算的角度来看，小区域更适合更好地适应非平稳性。然而，在实践中，需要大的区域来控制方差。我们提出了一种新的贝叶斯三步方法，允许较小的区域，而不会影响随后的方差增加。我们能够将不确定性从一个步骤传播到下一个步骤，而不会因为重用数据而导致问题。正如我们的模拟示例所示，推理的改进也会导致预测的改进。我们说明了这种新的方法在沙特阿拉伯的模拟高分辨率风速数据集。本文的补充文件可以在线获得。
ABSTRACT Environmental processes resolved at a sufficiently small scale in space and time inevitably display nonstationary behavior. Such processes are both challenging to model and computationally expensive when the data size is large. Instead of modeling the global non-stationarity explicitly, local models can be applied to disjoint regions of the domain. The choice of the size of these regions is dictated by a bias-variance trade-off; large regions will have smaller variance and larger bias, whereas small regions will have higher variance and smaller bias. From both the modeling and computational point of view, small regions are preferable to better accommodate the non-stationarity. However, in practice, large regions are necessary to control the variance. We propose a novel Bayesian three-step approach that allows for smaller regions without compromising the increase of the variance that would follow. We are able to propagate the uncertainty from one step to the next without issues caused by reusing the data. The improvement in inference also results in improved prediction, as our simulated example shows. We illustrate this new approach on a dataset of simulated high-resolution wind speed data over Saudi Arabia. Supplemental files for this article are available online.