An elaborate algorithm for analyzing the Borgonovo moment-independent sensitivity by replacing the probability density function estimation with the probability estimation

Borgonovo moment-independent sensitivity index (BMSI) was proposed to measure the sensitivity of model inputs according to the whole distribution of model output not only a specific moment. The main computational difficulty of the BMSI is to estimate the unconditional probability density function (PDF) and the conditional PDF of the model output. Generally, the estimation of cumulative distribution function (CDF) is easier than that of the PDF, but CDF-based method needs to calculate the extreme points of the differences between the unconditional PDF and the conditional PDF of model output. In addition, the computational cost of the existing CDF-based method also depends on the dimensionality of model inputs. To avoid these accessional computations, this paper derives a new formula by innovatively combining the law of total expectation in the successive intervals without overlapping and the Bayes theorem. The proposed new formula can obtain every input's BMSI only by one group of unconditional model inputs-output samples and does not need to estimate the PDF and the extreme points, which greatly reduces the computational difficulty of the BMSI by replacing the PDF estimation with the probability estimation. Four case studies are analyzed, and the results demonstrate the effectiveness of the proposed algorithm for estimating the BMSI.