Small sample sensitivity analysis techniques for computer models.with an application to risk assessment

TLDR

Modeling increasingly complex systems with hundreds of inputs is computationally expensive and mathematically intractable, making decision‑making under uncertainty challenging. The study aims to extend Latin hypercube sampling so that sensitivity analyses can be performed under uncertain input distributions without additional computer runs. A weighted Latin hypercube design is proposed, where input vectors are assigned probabilities reflecting distribution assumptions and the weights are also used in a modified nonparametric Friedman test; the method is demonstrated on a risk‑assessment model for geological radioactive waste disposal. The weighted design yields an unbiased estimate of the output cumulative distribution function and enables exploration of different input distribution assumptions without extra runs or response‑surface fitting.

Abstract

As modeling efforts expand to a broader spectrum of areas the amount of computer time required to exercise the corresponding computer codes has become quite costly (several hours for a single run is not uncommon). This costly process can be directly tied to the complexity of the modeling and to the large number of input variables (often numbering in the hundreds) Further, the complexity of the modeling (usually involving systems of differential equations) makes the relationships among the input variables not mathematically tractable. In this setting it is desired to perform sensitivity studies of the input-output relationships. Hence, a judicious selection procedure for the choic of values of input variables is required, Latin hypercube sampling has been shown to work well on this type of problem. However, a variety of situations require that decisions and judgments be made in the face of uncertainty. The source of this uncertainty may be lack ul knowledge about probability distributions associated with input variables, or about different hypothesized future conditions, or may be present as a result of different strategies associated with a decision making process In this paper a generalization of Latin hypercube sampling is given that allows these areas to be investigated without making additional computer runs. In particular it is shown how weights associated with Latin hypercube input vectors may be rhangpd to reflect different probability distribution assumptions on key input variables and yet provide: an unbiased estimate of the cumulative distribution function of the output variable. This allows for different distribution assumptions on input variables to be studied without additional computer runs and without fitting a response surface. In addition these same weights can be used in a modified nonparametric Friedman test to compare treatments, Sample size requirements needed to apply the results of the work are also considered. The procedures presented in this paper are illustrated using a model associated with the risk assessment of geologic disposal of radioactive waste.