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# Optimization of algorithms with respect to tuning parameters; upper panel: full ST algorithm; middle panel: HP algorithm, lower panel: Autometrics. Percentages correspond to averages over all EDGPs.

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Global sensitivity analysis is primarily used to investigate the effects of uncertainties in the input variables of physical models on the model output. This work investigates the use of global sensitivity analysis tools in the context of variable selection in regression models. Specifically, a global sensitivity measure is applied to a criterion o...

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... A brief history of the discipline can be found in [13], while recent reviews can be found in [14,15]. GSA has been applied to the study of variable selection in regression [16], suggesting a similar, though different, application to feature selection in ML. Whereas in [16] the emphasis was on finding a more efficient way of identifying a known data generating process, here the emphasis is on the interpretability of the results. ...

... GSA has been applied to the study of variable selection in regression [16], suggesting a similar, though different, application to feature selection in ML. Whereas in [16] the emphasis was on finding a more efficient way of identifying a known data generating process, here the emphasis is on the interpretability of the results. Note also that when performing a GSA, the question is not only which factors are influential, but also how they are influential, for example whether interactions are relevant and what is the effective dimension of the problem [17]. ...

... We estimate S T i using an estimator and a structured sample constructed as in [31]. This kind of estimator is employed also in [16] to rank regressors in terms of their importance in a regression model. Specifically, given the sample data {Y i , X i } let us consider γ RF models. ...

The present work provides an application of Global Sensitivity Analysis to supervised machine learning methods such as Random Forests. These methods act as black boxes, selecting features in high--dimensional data sets as to provide accurate classifiers in terms of prediction when new data are fed into the system. In supervised machine learning, predictors are generally ranked by importance based on their contribution to the final prediction. Global Sensitivity Analysis is primarily used in mathematical modelling to investigate the effect of the uncertainties of the input variables on the output. We apply it here as a novel way to rank the input features by their importance to the explainability of the data generating process, shedding light on how the response is determined by the dependence structure of its predictors. A simulation study shows that our proposal can be used to explore what advances can be achieved either in terms of efficiency, explanatory ability, or simply by way of confirming existing results.

... A brief history of the discipline can be found in [13], while recent reviews can be found in [14,15]. GSA has been applied to the study of variable selection in regression [16], suggesting a similar, though different, application to feature selection in ML. Whereas in [16] the emphasis was on finding a more efficient way of identifying a known data generating process, here the emphasis is on the interpretability of the results. ...

... GSA has been applied to the study of variable selection in regression [16], suggesting a similar, though different, application to feature selection in ML. Whereas in [16] the emphasis was on finding a more efficient way of identifying a known data generating process, here the emphasis is on the interpretability of the results. Note also that when performing a GSA, the question is not only which factors are influential, but also how they are influential, for example whether interactions are relevant and what is the effective dimension of the problem [17]. ...

... We estimate S T i using an estimator and a structured sample constructed as in [31]. This kind of estimator is employed also in [16] to rank regressors in terms of their importance in a regression model. Specifically, given the sample data {Y i , X i } let us consider γ RF models. ...

The present work provides an application of Global Sensitivity Analysis to supervised machine learning methods such as Random Forests. These methods act as black boxes, selecting features in high--dimensional data sets as to provide accurate classifiers in terms of prediction when new data are fed into the system. In supervised machine learning, predictors are generally ranked by importance based on their contribution to the final prediction. Global Sensitivity Analysis is primarily used in mathematical modelling to investigate the effect of the uncertainties of the input variables on the output. We apply it here as a novel way to rank the input features by their importance to the explainability of the data generating process, shedding light on how the response is determined by the dependence structure of its predictors. A simulation study shows that our proposal can be used to explore what advances can be achieved either in terms of efficiency, explanatory ability, or simply by way of confirming existing results.

... Model choice is also of primary concern in many areas of applied studies. Becker et al. (2021) has developped an approch of variable selection in regression models using global sensitivity analysis. Zhang et al. (2014) proposed propose a new variable selection method called logistic elastic net for the logistic regression model in pattern recognition. ...

In applied research in general, analysts frequently use variable selection methods in order to identify independent predictors of an outcome. The bootstrap method replaces complex analytical procedures by computer intensive empirical analysis. It relies heavily on Monte Carlo Method where several random resamples are drawn from a given original sample. The bootstrap method has been shown to be an effective technique in situations where it is necessary to determine the sampling distribution of (usually) a complex statistic with an unknown probability distribution using these data in a single sample. This work investigates the use of bootstrap tools in the context of variable selection in the generalized extreme value regression model. The treatment is based specifically upon drawing repeated bootstrap samples from the original dataset by founding the proportion of bootstrap samples in which each variable was identified as an independent predictor of the outcome. We performed a real data application and compared this approch with traditional model selection methods.

... Overall, the sensitivity analysis checking the ordinary least squares parameters for a beta coefficient suggests a linear approach to fit the method's robustness [135]. In summary, the sensitivity analysis would characterise the first-class definition of the input variables in this study, i.e., the variables are sufficient to define a robust econometric model that recognises all possible obstacles and proposes a trait prediction [136]. ...

This study considers diversification effects and significant influences on tourist arrivals as a vital export direction. Different quantitative methods, namely a cointegrated-autoregressive model, panels, sentiment and sensitivity analysis, were used in this study. The time-series data for Croatia and Slovenia were isolated from several secondary sources. The variables examined in this approach are tourist arrivals, precipitations, sunny days, earthquakes, microbes and CO2 emissions. The study results showed that there is a severe negative effect on tourist arrivals defined by viruses. Moreover, there is a significant decisive effect of weather conditions on tourist arrivals. Nevertheless, it is necessary to move past Covid-19 pandemic discussions to yield more accurate tourism supply forecasts, while demand is already somehow low since the beginning of 2020. The primary significance is to develop a broader thinking about the impacts of CO2 emissions on the tourism escorted to official tourist websites.

Highlights
• Advances of science and policy has deep but informal roots in sensitivity analysis.
• Modern sensitivity analysis is now evolving into a formal and independent discipline.
• New areas such data science and machine learning benefit from sensitivity analysis.
• Challenges, methodological progress, and outlook are outlined in this special issue.

Sensitivity analysis (SA) as a ‘formal’ and ‘standard’ component of scientific development and policy support is relatively young. Many researchers and practitioners from a wide range of disciplines have contributed to SA over the last three decades, and the SAMO (sensitivity analysis of model output) conferences, since 1995, have been the primary driver of breeding a community culture in this heterogeneous population. Now, SA is evolving into a mature and independent field of science, indeed a discipline with emerging applications extending well into new areas such as data science and machine learning. At this growth stage, this editorial leads a special issue consisting of one Position Paper on “The future of sensitivity analysis” and 11 research papers on “Sensitivity analysis for environmental modelling” published in Environmental Modelling & Software in 2020–21.

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.