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The Weather Risk Attribution Forecast (WRAF) is a forecasting tool that usesoutput from global climate models to make simultaneous attribution statementsabout whether and how greenhouse gas emissions have contributed to extremeweather across the globe. However, in conducting a large number of simultaneoushypothesis tests, the WRAF is prone to identifying false "discoveries." Acommon technique for addressing this multiple testing problem is to adjust theprocedure in a way that controls the proportion of true null hypotheses thatare 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 tomisspecification of the underlying statistical model. In this paper, we developa Bayesian decision theoretic approach for dependent multiple testing and anonparametric hierarchical statistical model that flexibly controls falsediscovery and is robust to model misspecification. We illustrate the robustnessof our procedure to model error with a simulation study, using a framework thataccounts for generic spatial dependence and allows the practitioner to flexiblyspecify the decision criteria. Finally, we apply our procedure to severalseasonal forecasts and discuss implementation for the WRAF workflow.

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