Sampling-Based Methods for Uncertainty and Sensitivity Analysis

Jon Helton
Sandia National Laboratories

Sampling-based methods for uncertainty and sensitivity analysis are reviewed.  The following topics are considered:  (i) Definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (ii) Generation of samples from uncertain analysis inputs, (iii) Propagation of sampled inputs through an analysis, (iv) Presentation of uncertainty analysis results, and (v) Determination of sensitivity analysis results. Special emphasis is given to possible approaches to sensitivity analysis, with brief discussions provided for the following procedures: examination of scatterplots, correlation and partial correlation analysis, regression analysis, rank transformations, tests for patterns based on grids, tests for patterns based on distance measures, nonparametric regression analysis, two dimensional Kolmogorov-Smirnov test, squared differences of ranks test, and complete variance decomposition. Sampling-based methods for uncertainty and sensitivity analysis are powerful tools for use in model and analysis verification. Specifically, the sampling-based uncertainty propagation forces an extensive exercise of the implementation of an analysis, and the sensitivity procedures facilitate a detailed examination of the relationships between analysis inputs and analysis results.

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