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

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.     

Sensitivity analysis and related analyses: A review of some statistical techniques

This paper reviews five related types of analysis, namely (i) sensitivity or what-if analysis, (ii) uncertainty or risk analysis, (iii) screening, (iv) validation, and (v) optimization. The main questions are: when should which type of analysis be applied; which statistical techniques may then be used? This paper claims that the proper sequence to follow in the evaluation of simulation models is as follows. 1) Validation, in which the availability of data on the real system determines which type of statistical technique to use for validation. 2) Screening: in the simulation‘s pilot phase the really important inputs can be identified through a novel technique, called sequential bifurcation, which uses aggregation and sequential experimentation. 3) Sensitivity analysis: the really important inputs should be subjected to a more detailed analysis, which includes interactions between these inputs; relevant statistical techniques are design of experiments (DOE) and regression analysis. 4) Uncertainty analysis: the important environmental inputs may have values that are not precisely known, so the uncertainties of the model outputs that result from the uncertainties in these model inputs should be quantified; relevant techniques are the Monte Carlo method and Latin hypercube sampling. 5) Optimization: the policy variables should be controlled; a relevant technique is Response Surface Methodology (RSM), which combines DOE, regression analysis, and steepest-ascent hill-climbing. The recommended sequence implies that sensitivity analysis procede uncertainty analysis. Several case studies for each phase are briefly discussed in this paper.     

New improvements in the use of dependence measures for sensitivity analysis and screening

ABSTRACT

Physical phenomena are commonly modelled by time consuming numerical simulators, function of many uncertain parameters whose influences can be measured via a global sensitivity analysis. The usual variance-based indices require too many simulations, especially as the inputs are numerous. To address this limitation, we consider recent advances in dependence measures, focusing on the distance correlation and the Hilbert–Schmidt independence criterion. We study and use these indices for a screening purpose. Numerical tests reveal differences between variance-based indices and dependence measures. Then, two approaches are proposed to use the latter for a screening purpose. The first approach uses independence tests, with existing asymptotic versions and spectral extensions; bootstrap versions are also proposed. The second considers a linear model with dependence measures, coupled to a bootstrap selection method or a Lasso penalization. Numerical experiments show their potential in the presence of many non-influential inputs and give successful results for a nuclear reliability application.