Forward-reverse switch between density-based and regional sensitivity analysis

Abstract

Global sensitivity analysis is a widely used tool for uncertainty apportionment and is very useful for decision making, risk assessment, model simplification, optimal design of experiments, etc. Density-based sensitivity analysis and regional sensitivity analysis are two widely used approaches. Both of them can work with a given sample set of model input-output pairs. One significant difference between them is that density-based sensitivity analysis analyzes output distributions conditional on input values (forward), while regional sensitivity analysis analyzes input distributions conditional on output values (reverse). In this paper, we study the relationship between these two approaches and show that regional sensitivity analysis (reverse), when focusing on probability density functions of input, converges towards density-based sensitivity analysis (forward) as the number of classes for conditioning model outputs in the reverse method increases. Similar to the existing general form of forward sensitivity indices, we derive a general form of the reverse sensitivity indices and provide the corresponding reverse given-data method. Due to the shown equivalence, the reverse given-data method provides an efficient way to approximate density-based sensitivity indices. Two test examples are used to verify this connection and compare the results. Finally, we use the reverse given-data method to perform sensitivity analysis in a carbon dioxide storage benchmark problem with multiple outputs, where forward analysis of density-based indices would be impossible due to the high-dimensionality of its model outputs.