Sampling methods and sensitivity analysis for large parameter sets
Models with large parameter (i.e., hundreds or thousands of parameters) often behave as if they depend upon only a few parameters, with the rest having comparatively little influence. One challenge of sensitivity analysis with such models is screening parameters to identify the influential ones, and then characterizing their influences. Large models often require significant computing resources to evaluate their output, and so a good screening mechanism should be efficient: it should minimize the number of times a model must be exercised. This paper describes an efficient procedure to perform sensitivity analysis on deterministic models with specified ranges or probability distributions for each parameter. It is based on repeated exercising of the model, which can be treated as a black box. Statistical checks can ensure that the screening identified parameters that account for the bulk of the model variation. Subsequent sensitivity analysis can use the screening information to reduce the investment required to characterize the influence of influential and other parameters. The procedure exploits simplifications in the dependence of a model output on model inputs. It works best where a small number of parameters are much more influential than all the rest. The method is much more sensitive to the number of influential parameters than to the total number of parameters. It is most effective when linear or quadratic effects dominate higher order effects and complex interactions. The paper presents a set of Mathematica functions that can be used to create a variety of types of experimental designs useful for sensitivity analysis, including simple random, latin hypercube and fractional factorial sampling. Each sampling method can use discretization, folding grouping and replication to create composite designs. These techniques have been combined in a composite approach called Iterated Fractional Factorial Design (IFFD). The procedure is applied to model of nuclear fuel waste disposal, and to simplified example models to demonstrate the concepts involved.
sensitivity analysis mathematica latin hypercube iterated fractional factorial design (iffd) computer models parameter screening simulation supersaturated design