Sensitivity analysis of input variables in generalized linear models

In today’s world, using the statistical modeling process, natural phenomena can be used to analyze and predict the events under study. ‎ Many hydrological modeling methods do not make the best use of available information because hydrological models show a wide range of environmental processes that complex the model‎‏. ‎‎‎‎In particular, when predicting, parameters affect the performance of statistical models. In many risk assessment issues, the presence of uncertainty in the parameters leads to uncertainty in predicting the model. Global sensitivity analysis is a tool used to show uncertainty and is used in decision making, risk assessment, model simplifcation and so on. Minkowski distance sensitivity analysis and regional sensitivity analysis are two broad methods that can work with a given sample set of model input-output pair. One signifcant difference between them is that minkowski distance sensitivity analysis analyzes output distributions conditional on input values (forward), while regional sensitivity analysis analyzes input distributions conditional on output values (reverse). In this dissertation, 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 minkowski distance 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. Finally, the sensitivity analysis of a water storage design with high dimensions of the model outputs is performed.