In most application fields, analysts support their investigations through the use of quantitative models. Over the years, the computation of sensitivity (or importance) measures has become an integrating part of the analysis, allowing analysts to obtain insights on key drivers of model behavior either on a local or on a global scale. However, the estimation of global sensitivity measures may become a computationally challenging task, especially when the number of model inputs is large and the model output is sparse. Moreover, the estimation is considered even more challenging when the sensitivity measures require to look at the entire model output distribution. Most of the algorithms to compute sensitivity measures require special sampling schemes or additional model evaluations so that available data from previous model runs (e.g., from an uncertainty analysis based on Latin Hypercube Sampling) cannot be reused. In this MS, we are interested in the challenging task of estimating global sensitivity measures by recycling an available finite set of input/output data. Green sensitivity, by recycling, avoids wasting. Different global sensitivity measures are proposed by the authors, depending on the application field and the associated constraints: moment-independent sensitivity measures, quantile-oriented sensitivity measures, Shapley effects. Various statistical estimation procedures are studied, such as, e.g., nearest-neighbour techniques, random forest or bayesian statistics.
14:00
Integrated Distribution Functions (with Friends and Relatives) for Sensitivity Analysis
Elmar Plischke | Institute of Disposal Reasearch, Clausthal University of Technology | Germany
Show details
Authors:
Elmar Plischke | Institute of Disposal Reasearch, Clausthal University of Technology | Germany
Giovanni Rabitti | Department of Decision Sciences, Uni Bocconi | Italy
Emanuele Borgonovo | Department of Decision Sciences, Uni Bocconi | Italy
Moment-independent sensitivity measures offer insights even when linear regression-based or functional
dependence-based measures may fail. However, the quest for a robust measure from the
class of moment-independent sensitivity measures is still ongoing. In this work, we discuss integrated
distribution function-based measures. By definition they are continuously differentiable,
so that they can be treated computationally effective also when estimating them from available
input/output data. Links to the sensitivity of quantiles and expectiles are also established.
14:30
Random forest-based estimation of Quantile Oriented Sensitivity Analysis
Kévin Elie-Dit-Cosaque | Université Lyon 1, SCOR SE | France
Show details
Authors:
Kévin Elie-Dit-Cosaque | Université Lyon 1, SCOR SE | France
Véronique Maume-Deschamps | Université Lyon 1 | France
Ecaterina Nisipasu | SCOR SE | France
The standard quantitative methods of the Global Sensitivity Analysis of a numerical model, Y = f(X) with
d random inputs X = (X_1,...,X_d), consists in quantifying the contributions of each of its input
parameters in the variability of its output such as Sobol’ indices or Shapley effects.
The indices cited above are useful tools of Sensitivity Analysis if one is interested in a particular characteristic
of the Y distribution: the mean E[Y] of the numerical model. Indeed, they allow to quantify which variables
have the greatest influence on the mean by using variance as a measure of distance. However, if we consider another
characteristic of the Y distribution as quantity of interest, for example, a quantile of order alpha, it seems
very intuitive to expect an extreme quantile to be sensitive to very different variables than the average.
As a result, when the quantity of interest is the quantile of order alpha of the Y distribution, adapted indices
named QOSA (Quantile Oriented Sensitivity Analysis) based on a contrast function were developed in order to determine
the most influential variables.
Estimators have been proposed to estimate the QOSA indices but these remain cumbersome to handle and are based
on kernel estimation methods (problem with optimal bandwidth selection). We then propose a new estimation method
based on the random forest allowing to estimate efficiently the QOSA indices.
15:00
Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution
Baptiste Broto | CEA, LIST, Université Paris-Saclay | France
Show details
Authors:
Baptiste Broto | CEA, LIST, Université Paris-Saclay | France
François Bachoc | Institut de Mathématiques de Toulouse, Université Paul Sabatier | France
Marine Depecker | CEA, LIST, Université Paris-Saclay | France
The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model f. They are linear combinations of the Sobol’ indices defined with dependent inputs.
When the input distribution is known, we investigate the already existing estimator defined in « E. Song, B. Nelson, and J. Staum, Shapley Effects for Global Sensitivity Analysis: Theory and Computation, SIAM/ASA Journal on Uncertainty Quantification, (2016) » and suggest a new one which optimizes the accuracy of the estimates of the Sobol indices.
Then, we assume that we only observe an i.i.d. sample X_n, n=1, …, N of the input vector X and that we have access to the computer code f. We extend the double Monte-Carlo and Pick-and-Freeze estimators of the Sobol’ indices in this case and show their consistency in a really general framework. We also provide rates of convergence for continuous input variables. We then give the consistency of the implied estimators of the Shapley effects. We also apply one of these estimators to a real data set with categorical and continuous input variables.
15:30
- CANCELED - Bayesian Estimation of Probabilistic Sensitivity Measures for Computer Experiments
Xuefei Lu | Department of Energy, Politecnico di Milano and Department of Decision Sciences, Bocconi University, Milan | Italy
Show details
Authors:
Isadora Antoniano-Villalobos | Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari University of Venice and Bocconi Institute for Data Science and Analytics (BIDSA), Bocconi University, Milan | Italy
Emanuele Borgonovo | Bocconi University, Milan | Italy
Xuefei Lu | Department of Energy, Politecnico di Milano and Department of Decision Sciences, Bocconi University, Milan | Italy
Simulation-based experiments are becoming increasingly important in scientific investigations. Global sensitivity analysis is used to quantify the effects of inputs (individual or groups thereof) onto the response of the model output. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of uncertainty. We propose a Bayesian alternative for the estimation of probabilistic sensitivity measures based on a given sample. The estimator of both variance-based and moment-independent sensitivity measures can be derived, even at higher orders. The Bayesian paradigm allows the quantification of the uncertainty in the estimates of probabilistic sensitivity measures without requiring additional simulator evaluations. The estimator is applied to a series of numerical experiments, including both deterministic and stochastic simulators as well as a realistic application.