Implementing the Linear Adaptive False Discovery Rate Procedure for Spatiotemporal Trend Testing

Statistical inference in spatiotemporal trend analysis often involves testing separate hypotheses for each pixel in datasets containing thousands of observations. A pixel is considered significant if its p-value falls below a rejection threshold (α). However, this uncorrected approach ignores the large number of simultaneous tests and greatly increases the risk of false positives. This issue, known as multiple testing or multiplicity, can be addressed by controlling the false discovery rate (FDR), defined as the expected proportion of false positives (i.e., false discoveries) among all rejected hypotheses, at a pre-specified control level q. This study implements the linear adaptive two-stage Benjamini–Krieger–Yekutieli (BKY) procedure for FDR control in spatiotemporal trend testing and compares it with two alternatives: the uncorrected significance approach and the original non-adaptive Benjamini–Hochberg (BH) procedure. The BKY method empirically estimates the number of true null hypotheses (m0) and adaptively relaxes the rejection threshold when many true alternatives are present, thereby increasing statistical power without compromising FDR control. Results indicate that the BKY procedure is a recommended approach for large-scale trend testing using spatiotemporal environmental data, particularly in gridded-data-intensive fields such as environmental remote sensing, climatology, and hydrology. To foster reproducibility, R code is provided to apply the BKY procedure and compare it with the uncorrected raw p-values and the BH approach on any gridded dataset.