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A comparison of methods for representing and aggregating uncertainties involving sparsely sampled random variables -final results1

Romero, Vicente J.; Swiler, Laura P.; Urbina, Angel U.

This paper discusses the treatment of uncertainties corresponding to relatively few samples of random-variable quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse samples it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem an interesting and difficult one. In this paper the performance of five uncertainty representation techniques is characterized on twenty-one test problems (over thousands of trials for each problem) according to these two opposing objectives and other performance measures. Two of the methods exhibit significantly better overall performance than the others according to the objectives and performance measures emphasized. © 2012 AIAA.