Global Sensitivity and Domain-Selective Testing for Functional-Valued Responses: An Application to Climate Economy Models

Complex computational models are increasingly used by business and governments for making decisions, such as how and where to invest to transition to a low carbon world. Complexity arises with great evidence in the outputs generated by large scale models, and calls for the use of advanced Sensitivity Analysis techniques. To our knowledge, there are no methods able to perform sensitivity analysis for outputs that are more complex than scalar ones and to deal with model uncertainty using a sound statistical framework. The aim of this work is to address these two shortcomings by combining sensitivity and functional data analysis. We express output variables as smooth functions, employing a Functional Data Analysis (FDA) framework. We extend global sensitivity techniques to function-valued responses and perform significance testing over sensitivity indices. We apply the proposed methods to computer models used in climate economics. While confirming the qualitative intuitions of previous works, we are able to test the significance of input assumptions and of their interactions. Moreover, the proposed method allows to identify the time dynamics of sensitivity indices.