Multivariate Global Sensitivity Analysis Based on Distance Components Decomposition

In this article, a new set of multivariate global sensitivity indices based on distance components decomposition is proposed. The proposed sensitivity indices can be considered as an extension of the traditional variance-based sensitivity indices and the covariance decomposition-based sensitivity indices, and they have similar forms. The advantage of the proposed sensitivity indices is that they can measure the effects of an input variable on the whole probability distribution of multivariate model output when the power of distance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>α</mml:mi> <mml:mo><</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:math> . When <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:math> , the proposed sensitivity indices are equivalent to the covariance decomposition-based sensitivity indices. To calculate the proposed sensitivity indices, an efficient Monte Carlo method is proposed, which can also be used to calculate the covariance decomposition-based sensitivity indices at the same time. The examples show the reasonability of the proposed sensitivity indices and the stability of the proposed Monte Carlo method.

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