Premium
A Stable Approach Based on Asymptotic Space Integration for Moment‐Independent Uncertainty Importance Measure
Author(s) -
Xu Xin,
Lu Zhenzhou,
Luo Xiaopeng
Publication year - 2014
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.12087
Subject(s) - measure (data warehouse) , mathematics , moment (physics) , probability density function , cumulative distribution function , dimension (graph theory) , rate of convergence , convergence (economics) , numerical integration , mathematical optimization , probability distribution , representation (politics) , propagation of uncertainty , function (biology) , moment generating function , computation , computer science , algorithm , statistics , key (lock) , mathematical analysis , data mining , computer security , law , economic growth , biology , classical mechanics , evolutionary biology , political science , physics , politics , pure mathematics , economics
The error estimate of Borgonovo's moment‐independent index δ i is considered, and it shows that the possible computational complexity of δ 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, δ 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 δ 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.