The statistical analysis of environmental data from remote sensing and Earth system simulations often entails the analysis of gridded spatio-temporal data, with a hypothesis test being performed for each grid cell. When the whole image or a set of grid cells are analyzed for a global effect, the problem of multiple testing arises. When no global effect is present, we expect \( \alpha \)% of all grid cells to be false positives, and spatially autocorrelated data can give rise to clustered spurious rejections that can be misleading in an analysis of spatial patterns. In this work, we review standard solutions for the multiple testing problem and apply them to spatio-temporal environmental data. These solutions are independent of the test statistic, and any test statistic can be used (e.g., tests for trends or change points in time series). Additionally, we introduce permutation methods and show that they have more statistical power. Real-world data are used to provide examples of the analysis, and the performance of each method is assessed in a simulation study. Unlike other simulation studies, our study compares the statistical power of the presented methods in a comprehensive simulation study. In conclusion, we present several statistically rigorous methods for analyzing spatio-temporal environmental data and controlling the false positives. These methods allow the use of any test statistic in a wide range of applications in environmental sciences and remote sensing.

中文翻译：

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在时空环境数据分析中考虑多次测试

来自遥感和地球系统模拟的环境数据的统计分析通常需要对网格化的时空数据进行分析，并对每个网格单元进行假设检验。当分析整个图像或一组网格单元的全局效果时，就会出现多次测试的问题。当不存在全局影响时，我们期望\（\ alpha \）所有网格单元中有％为假阳性，并且空间自相关数据可能会导致聚集的虚假拒绝，这些虚假拒绝在空间模式分析中可能会产生误导。在这项工作中，我们将审查针对多重测试问题的标准解决方案，并将其应用于时空环境数据。这些解决方案独立于测试统计量，并且可以使用任何测试统计量（例如，测试趋势或时间序列中的变化点）。此外，我们介绍了置换方法，并表明它们具有更大的统计能力。实际数据用于提供分析示例，并且在模拟研究中评估每种方法的性能。与其他模拟研究不同，我们的研究在全面的模拟研究中比较了所提出方法的统计能力。结论，我们提出了几种统计上严格的方法来分析时空环境数据并控制误报。这些方法允许在环境科学和遥感的广泛应用中使用任何检验统计量。