Speaker: Bo Li, Marjorie Roberts Professor and Chair, Department of Statistics, University of Illinois Urbana-Champaign

Title: Multiple Testing for Spatial Extremes with Application to Climate Model Evaluation

Abstract: Climate models are the primary tools for scientists to study why the Earth's climate is changing and how it might change in the future. An interesting question is how to evaluate whether a climate model simulates the Earth's real climate. Comparing two climate fields sheds light on climate model validation. While most of climate field comparisons focused on the mean and dependency of climate process, we focus on marginal extreme behavior including marginal extreme value distribution and return levels that often have devastating impacts on our ecosystems and societies. In particular, we aim to identify where the two climate extreme fields exhibit different marginal distributions, which can be more informative than a global measure of difference. This task requires multiple testing techniques to simultaneously evaluate the differences over all spatial locations. The large variation inherited in extreme model fitting makes the evaluation in climate extremes more challenging than that for mean and dependency structure. We propose a new multiple testing procedure, bivariate conditional local FDR (BiCLfdr), to efficiently detect signals from the highly variable but spatially correlated hypotheses. Our method takes into account both the large scale spatial variability and local spatial correlation to enhance the power for comparing marginal extreme distribution of two spatial extremes. We apply our method to identify where a regional climate model fails to represents the real extreme behavior of winter precipitation. This will provide climate scientists insights on how to improve climate models.