Abstract

Comparing the spatial characteristics of spatiotemporal random fields is often at demand. However, the comparison can be challenging due to the high-dimensional feature and dependency in the data. We develop a new multiple testing approach to detect local differences in the spatial characteristics of two spatiotemporal random fields by taking the spatial information into account. Our method adopts a two-component mixture model for location wise p-values and then derives a new false discovery rate (FDR) control, called mirror procedure, to determine the optimal rejection region. This procedure is robust to model misspecification and allows for weak dependency among hypotheses. To integrate the spatial heterogeneity, we model the mixture probability as well as study the benefit if any of allowing the alternative distribution to be spatially varying. An EM-algorithm is developed to estimate the mixture model and implement the FDR procedure. We study the FDR control and the power of our new approach both theoretically and numerically, and apply the approach to compare the mean and teleconnection pattern between two synthetic climate fields. Supplementary materials for this article are available online.

摘要

通常需要比较时空随机场的空间特征。然而，由于数据中的高维特征和依赖性，比较可能具有挑战性。我们开发了一种新的多重测试方法，通过考虑空间信息来检测两个时空随机场的空间特征的局部差异。我们的方法采用二元混合模型进行位置p-values，然后导出一个新的错误发现率 (FDR) 控制，称为镜像过程，以确定最佳拒绝区域。该过程对于模型错误指定是稳健的，并且允许假设之间的弱依赖性。为了整合空间异质性，我们对混合概率进行建模，并研究允许替代分布在空间上变化的任何好处。开发了一种 EM 算法来估计混合模型并实施 FDR 程序。我们从理论上和数值上研究了 FDR 控制和我们的新方法的力量，并将该方法应用于比较两个合成气候场之间的平均和遥相关模式。本文的补充材料可在线获取。