Survey of sampling-based methods for uncertainty and sensitivity analysis

TLDR: Sampling-based methods for uncertainty and sensitivity analysis are reviewed and special attention is given to the determination of sensitivity analysis results.

About: This article is published in Reliability Engineering & System Safety.The article was published on 2006-06-01 and is currently open access. It has received 1179 citations till now. The article focuses on the topics: Sensitivity analysis & Uncertainty analysis.

Figures

Table 10. Comparison of Formal Statistical and Monte Carlo Determination of p-Values for the SI Test and the Two Dimensional KS Test for Pressure (WAS_PRES) at 10,000 yr under Undisturbed (i.e., E0) Conditions (Fig. 5a) and Disturbed (i.e., E2) Conditions (Fig. 10a)

Fig. 8. Illustration of correlation coefficients: (a) c(xj, y) = 0.75 with xj = HALPOR and y = REP_SATB (left frame), and (b) c(xj, y) = −0.41 with xj = WGRCOR and y = REP_SATB (right frame).

Fig. 3. Examples of rank correlations of 0.00, 0.25, 0.50, 0.75, 0.90 and 0.99 imposed with the Iman/Conover restricted pairing technique for an LHS of size nS = 1000 (Fig. 5.1, Ref. 138).

Fig. 5. Representation of uncertainty in analysis results that are functions: (a, b) Pressure as a function of time (Figs. 7.5, 7.9, Ref. 101), and (c, d) Effects of aleatory uncertainty summarized as a CCDF (Fig. 10.5, Ref. 101).

Table 13. Sensitivity Analysis with the TDCC for Three Replicated Random Samples of Size 100 for Cumulative Brine Flow into Repository (BRNREPTC) at 1000 yr under Undisturbed (i.e., E0) Conditions (adapted from Table 9, Ref. 125)

Table 4. Comparison of Stepwise Regression Analyses with Raw and Rank-Transformed Data for Cumulative Brine Inflow to Vicinity of Repository over 10,000 yr from Anhydrite Marker Beds (BRAALIC) Under Undisturbed (i.e., E0) Conditions in Fig. 4b (Table 8.8, Ref. 101).

Frequently asked questions

Q1. What is the expression in Eq. (6-46)?

The expression in Eq. (6-46) is an additive model with the quantities αsx replacing the elements xj of x as the independent variables. 

Q2. What is the demanding part of a sampling-based uncertainty and sensitivity analysis?

17Propagation of the sample through the analysis to produce the mapping [xi, y(xi))], i = 1, 2, …, nS, from analysis inputs to analysis results is often the most computationally demanding part of a sampling-based uncertainty and sensitivity analysis. 

Q3. What is the common way to present the results of an uncertainty analysis?

19Presentation of uncertainty analysis results is generally straight forward and involves little more than displaying the results associated with the already calculated mapping [xi, y(xi)], i = 1, 2, …, nS. Presentation possibilities include means and standard deviations, density functions, cumulative distribution function (CDFs), complementary cumulative distribution functions (CCDFs), and box plots. 

Q4. What is the advantage of distance-based tests for patterns?

Distance-based tests for patterns have a potential advantage over grid-based tests in that they do not require the definition and use of a grid that can possibly influence the outcome of the test. 

Q5. What is the sensitivity analysis procedure used to illustrate?

the fluid flow model that has been used to illustrate other sensitivity analysis procedures is too computationally demanding for use with the procedures discussed in this section. 

Q6. What are the main reasons for the need for alternative representations for uncertainty?

Alternative representations for uncertainty such as evidence theory and possibility theory merit consideration for their potential to represent uncertainty in situations where little information is available. 

Q7. What is the role of probabilistic characterizations in a sensitivity analysis?

when limited information is available with which to characterize uncertainty, probabilistic characterizations can give the appearance of more knowledge than is really present. 

Q8. What is the reason why importance sampling complicates sensitivity analysis?

importance sampling complicates sensitivity analysis (Sect. 6) as the individual sample elements do not have equal weight (i.e., likelihood of occurrence). 

Q9. What is the correlation coefficient between xj and y?

As a correlation of 0 only indicates the absence of a linear association between xj and y, it does not preclude the existence of a well-defined nonlinear relationship between xj and y (e.g., y = sin xj). 

Q10. What is the importance of characterization of uncertainty in analysis inputs?

The appropriate characterization of the uncertainty in analysis inputs is essential to the performance of a meaningful uncertainty and sensitivityanalysis (Sect. 2). 

Q11. What is the reason why the partial correlation analyses in Fig. 10b fail?

The partial correlation analyses summarized in Fig. 10b fail at later times because the pattern appearing in Fig. 6b is too complex to be captured with a partial correlation analysis based on raw or rank-transformed data; analyses with SRCs or SRRCs also fail for the same reason.