Technological developments and open data policies have made large, global
environmental datasets accessible to everyone. For analysing such datasets,
including spatiotemporal correlations using traditional models based on
Gaussian processes does not scale with data volume and requires strong
assumptions about stationarity, separability, and distance measures of
covariance functions that are often unrealistic for global data. Only very few
modeling approaches suitably model spatiotemporal correlations while addressing
both computational scalability as well as flexible covariance models. In this
paper, we provide an extension to the multi-resolution approximation (MRA)
approach for spatiotemporal modeling of global datasets. MRA has been shown to
be computationally scalable in distributed computing environments and allows
for integrating arbitrary user-defined covariance functions. Our extension adds
a spatiotemporal partitioning, and fitting of complex covariance models
including nonstationarity with kernel convolutions and spherical distances. We
evaluate the effect of the MRA parameters on estimation and spatiotemporal
prediction using simulated data, where computation times reduced around two
orders of magnitude with an increase of the root-mean-square prediction error
of around five percent. This allows for trading off computation times against
prediction errors, and we derive a practical strategy for selecting the MRA
parameters. We demonstrate how the approach can be practically used for
analyzing daily sea surface temperature and precipitation data on global scale
and compare models with different complexities in the covariance function.

本文提出了一种针对全球数据的时空建模扩展方法，将多分辨率逼近（MRA）方法与分区及复杂协方差模型拟合相结合，实现了可扩展的计算性能和灵活的协方差模型，为分析全球性数据提供了实用的策略。

用于分析全球环境数据的时空多分辨率逼近

Spatiotemporal Multi-Resolution Approximations for Analyzing Global  Environmental Data

Automated sensing instruments on satellites and aircraft have enabled the
collection of massive amounts of high-resolution observations of spatial fields
over large spatial regions. If these datasets can be efficiently exploited,
they can provide new insights on a wide variety of issues. However, traditional
spatial-statistical techniques such as kriging are not computationally feasible
for big datasets. We propose a multi-resolution approximation (M-RA) of
Gaussian processes observed at irregular locations in space. The M-RA process
is specified as a linear combination of basis functions at multiple levels of
spatial resolution, which can capture spatial structure from very fine to very
large scales. The basis functions are automatically chosen to approximate a
given covariance function, which can be nonstationary. All computations
involving the M-RA, including parameter inference and prediction, are highly
scalable for massive datasets. Crucially, the inference algorithms can also be
parallelized to take full advantage of large distributed-memory computing
environments. In comparisons using simulated data and a large satellite
dataset, the M-RA outperforms a related state-of-the-art method.

本文提出了一种多分辨率逼近方法 (M-RA) 来处理具有不同空间坐标观测值的高斯过程，并基于多尺度基函数对空间结构进行建模。该方法既适用于参数推断，又适用于大规模数据集的预测，并且可以在分布式计算环境下实现并行化。通过模拟数据和卫星数据集的比较实验，M-RA 方法表现出优越的性能。