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Publication
Data-driven and Active Learning of Variance-based Sensitivity Indices with Bayesian Probabilistic Integration
Journal Contribution - Journal Article
Variance-based sensitivity indices play an important role in scientific computation and data mining, thus
the significance of developing numerical methods for efficient and reliable estimation of these sensitivity
indices based on (expensive) computer simulators and/or data cannot be emphasized too much. In this
article, the estimation of these sensitivity indices is treated as a statistical inference problem. Two principle
lemmas are first proposed as rules of thumb for making the inference. After that, the posterior features
for all the (partial) variance terms involved in the main and total effect indices are analytically derived
(not in closed form) based on Bayesian Probabilistic Integration (BPI). This forms a data-driven method
for estimating the sensitivity indices as well as the involved discretization errors. Further, to improve
the efficiency of the developed method for expensive simulators, an acquisition function, named Posterior
Variance Contribution (PVC), is utilized for realizing optimal designs of experiments, based on which an
adaptive BPI method is established. The application of this framework is illustrated for the calculation of
the main and total effect indices, but the proposed two principle lemmas also apply to the calculation of
interaction effect indices. The performance of the development is demonstrated by a illustrative numerical
example and three engineering benchmarks with finite element models.
Journal: Mechanical Systems and Signal Processing
ISSN: 0888-3270
Volume: 163
Publication year:2022
Accessibility:Open