Synopsis: The project was to develop the Bell Curve Calculus, which arithmetic operations were applied to a domain of Gaussians instead of numbers. This calculus was used to record the uncertainty in numerical calculations. It is similar to interval arithmetic, except that not all points in the interval are equally probable. The main application was to the propagation of quality of service properties, such as run-time, in e-Science and other workflows.
Hypotheses: That a Bell Curve Calculus can be built in which the results of arithmetic operations on Gaussians can be approximated sufficiently well by other Gaussians that the resulting calculus can be used to propagate numeric quality of service properties around workflows to provide reliable quality estimate.
Evaluation: Given the mean and standard deviation of the input Gaussians, those of the input Gaussians were experimentally approximated for the range of arithmetic operations needed in various quality of service calculations. The resulting calculus was successfully evaluated on some typical workflows.