Large-scale simultaneous hypothesis testing in monitoring carbon content from French soil database - A semi-parametric mixture approach

Investigating the information of the French National Soil Tests database for soil monitoring produces multiple hypothesis testing problems with hundreds or thousands of test responses to consider simultaneously. A largely used concept of error control in such multiple testing is the expected proportion of falsely rejected hypotheses, or False Discovery Rate (FDR). A related notion of local FDR (ℓFDR) can be appropriately represented by considering that the observed p-values come from a two-component mixture model where the component corresponding to the null hypothesis is known. In this work, we explore different solutions for FDR estimation. In particular, we introduce a specific version of a semi-parametric Expectation-Maximization (EM) algorithm for ℓFDR estimation, and compare it to classical ℓFDR estimation using parametric mixtures, and conventional FDR approaches. The performances of the different models for estimating the FDR and related criteria are first illustrated on the results of simulated multiple comparison tests. These approaches are then applied to soil carbon content monitoring on our database. The results show that not taking into account the FDR estimation can lead to over-estimation of the number of cantons (locations) subject to a significant change. However, we have detected large numbers of significant changes in the database that occurred during the time period of this study. Globally, losses in organic carbon are observed in Northern France, along the Atlantic coastal regions, and to a lesser extent for the data collected over the North-Eastern regions. The OC increases are more scattered over the territory. We also use the data to estimate the minimum number of samples needed at each period to detect a given change.