This article develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both point-wise and cluster-wise spatial analyses, and derive oracle procedures which optimally control the false discovery rate, false discovery exceedance and false cluster rate, respectively. A data-driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain. Our multiple testing procedures are asymptotically valid and can be effectively implemented using Bayesian computational algorithms for analysis of large spatial data sets. Numerical results show that the proposed procedures lead to more accurate error control and better power performance than conventional methods. We demonstrate our methods for analyzing the time trends in tropospheric ozone in eastern US.

中文翻译：

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大规模空间多重测试中的错误发现控制。


本文开发了一个统一的理论和计算框架，用于空间信号多重测试中的错误发现控制。我们考虑逐点和逐簇空间分析，并推导出分别最佳控制错误发现率、错误发现超出和错误聚类率的预言程序。开发了数据驱动的有限逼近策略来模拟连续空间域上的预言程序。我们的多个测试程序是渐近有效的，并且可以使用贝叶斯计算算法有效地实现，以分析大型空间数据集。数值结果表明，所提出的方法比传统方法具有更准确的误差控制和更好的功率性能。我们展示了分析美国东部对流层臭氧时间趋势的方法。