Environmental processes resolved at a sufficiently small scale in space and time will inevitably display non-stationary 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 data set of simulated high-resolution wind speed data over Saudi Arabia.

中文翻译：

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改进大数据集中的贝叶斯局部空间模型

在足够小的空间和时间尺度上解决的环境过程将不可避免地表现出非平稳行为。当数据量很大时，这样的过程既难以建模又计算昂贵。可以将局部模型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，小区域更可取以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。我们提出了一种新颖的贝叶斯三步法，它允许较小的区域，而不会影响随之而来的方差的增加。我们能够将不确定性从一个步骤传播到另一个步骤，而不会因重复使用数据而导致问题。正如我们的模拟示例所示，推理的改进也导致预测的改进。我们在沙特阿拉伯上空模拟高分辨率风速数据的数据集上说明了这种新方法。