Journal
RISK ANALYSIS
Volume 34, Issue 2, Pages 235-251Publisher
WILEY
DOI: 10.1111/risa.12087
Keywords
Asymptotic space integration; global sensitivity analysis; importance measure; moment-independent; uncertainty analysis
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Funding
- National Natural Science Foundation of China [51175425]
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The error estimate of Borgonovo's moment-independent index i is considered, and it shows that the possible computational complexity of i is mainly due to the probability density function (PDF) estimate because the PDF estimate is an ill-posed problem and its convergence rate is quite slow. So it reminds us to compute Borgonovo's index using other methods. To avoid the PDF estimate, i, which is based on the PDF, is first approximatively represented by the cumulative distribution function (CDF). The CDF estimate is well posed and its convergence rate is always faster than that of the PDF estimate. From the representation, a stable approach is proposed to compute i with an adaptive procedure. Since the small probability multidimensional integral needs to be computed in this procedure, a computational strategy named asymptotic space integration is introduced to reduce a high-dimensional integral to a one-dimensional integral. Then we can compute the small probability multidimensional integral by adaptive numerical integration in one dimension with an improved convergence rate. From the comparison of numerical error analysis of some examples, it can be shown that the proposed method is an effective approach to uncertainty importance measure computation.
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