Stochastic partial differential equation based modelling of large space–time data sets
Stochastic partial differential equation based modelling of large space–time data sets
复制标题
基于随机偏微分方程的大型时空数据集建模
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
W. Stahel
中科院分区：
文献类型：
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作者：
Fabio Sigrist;H. Künsch;W. Stahel
在空间和时间上，越来越大的过程数据集要求能够科普这些数据的统计模型和方法。我们发现，随机对流扩散偏微分方程的解决方案提供了一个灵活的模型类的时空过程，这是计算上可行的，也为大型数据集。通过随机偏微分方程定义的高斯过程通常具有不可分离的协方差结构。它的参数可以被物理地解释为明确地模拟现象，如在从环境科学到生态学的不同领域的许多自然过程中发生的传输和扩散。为了获得计算效率高的统计算法，我们使用谱方法来解决随机偏微分方程。这具有近似误差不随时间累积的优点，并且在谱空间中计算成本随维度线性增长，贝叶斯或频率论推理的总计算成本由快速傅立叶变换支配。该模型适用于降水预报的后处理从数值天气预报模式为北方瑞士。与数值模型的原始预测相比，后处理预测经过校准并量化了预测的不确定性。此外，它们的表现优于原始预测，因为它们的平均绝对误差较低。
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection–diffusion partial differential equation provides a flexible model class for spatiotemporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has, in general, a non‐separable covariance structure. Its parameters can be physically interpreted as explicitly modelling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. To obtain computationally efficient statistical algorithms, we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational cost of Bayesian or frequentist inference being dominated by the fast Fourier transform. The model proposed is applied to post‐processing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast with the raw forecasts from the numerical model, the post‐processed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error.
影响因子：
5.8
作者：
C. Paciorek
通讯作者：
C. Paciorek
影响因子：
3.2
作者：
P. Friederichs;A. Hense
通讯作者：
P. Friederichs;A. Hense