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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.

This paper1 explores some of the important considerations in devising a practical and consistent framework and methodology for working with experiments and experimental data in connection with modeling and prediction. The paper outlines a pragmatic and versatile “real-space” approach within which experimental and modeling uncertainties (correlated and uncorrelated, systematic and random, aleatory and epistemic) are treated to mitigate risk in modeling and prediction. The elements of data conditioning, model conditioning, model validation, hierarchical modeling, and extrapolative prediction under uncertainty are examined. An appreciation can be gained for the constraints and difficulties at play in devising a viable end-to-end methodology. The considerations and options are many, and a large variety of viewpoints and precedents exist in the literature, as surveyed here. Rationale is given for the various choices taken in assembling the novel real-space end-to-end framework.