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Applications and Case Studies

Spatially Dependent Multiple Testing Under Model Misspecification, With Application to Detection of Anthropogenic Influence on Extreme Climate Events

, &
Pages 61-78
Received 01 Apr 2017
Accepted author version posted online: 02 Apr 2018
Published online: 11 Jul 2018


The Weather Risk Attribution Forecast (WRAF) is a forecasting tool that uses output from global climate models to make simultaneous attribution statements about whether and how greenhouse gas emissions have contributed to extreme weather across the globe. However, in conducting a large number of simultaneous hypothesis tests, the WRAF is prone to identifying false “discoveries.” A common technique for addressing this multiple testing problem is to adjust the procedure in a way that controls the proportion of true null hypotheses that are incorrectly rejected, or the false discovery rate (FDR). Unfortunately, generic FDR procedures suffer from low power when the hypotheses are dependent, and techniques designed to account for dependence are sensitive to misspecification of the underlying statistical model. In this article, we develop a Bayesian decision-theoretical approach for dependent multiple testing and a nonparametric hierarchical statistical model that flexibly controls false discovery and is robust to model misspecification. We illustrate the robustness of our procedure to model error with a simulation study, using a framework that accounts for generic spatial dependence and allows the practitioner to flexibly specify the decision criteria. Finally, we apply our procedure to several seasonal forecasts and discuss implementation for the WRAF workflow. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Supplementary Materials

The appendices to this paper contain an overview of classical decision theory approaches for false discovery control, a set of supplemental figures, specific details on the skew-t parameterization used in the article, prior specification for all Bayesian models, details on Markov chain Monte Carlo methods, and supporting information for the simulation study.

Additional information


This research was supported by the Director, Office of Science, Office of Biological and Environmental Research of the U.S. Department of Energy under contract no. DE-AC02-05CH11231 and used resources of the National Energy Research Scientific Computing Center (NERSC), also supported by the Office of Science of the U.S. Department of Energy, under contract no. DE-AC02-05CH11231.

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