Euradwaste '08 - EU Bookshop - Europa

ony, interactions, etc., and to check the importance of sample size. The second step consists in analysing
a simplified, though representative, PA model. The complex input-output relation, characterised
by strong interactions among input parameters, makes it a challenging model to test SA techniques.
In this case, the target is twofold: firstly to compare different options within a given SA
techniques (to study the added value of using more complex versions of a given technique – classical
FAST versus extended FAST, first order regressions versus higher order regressions, etc.-), and
secondly to cross-compare the results obtained using different techniques. Finally, different SA
techniques will be used to analyse PA results obtained by different partners (number of parameters
ranging from a few to some a hundred).
The structure of this paper is as follows. In section 2 we review most important screening and
global methods and discuss about their advantages and disadvantages. Section 3 is dedicated to describe
the Sensitivity Analysis Benchmark developed under PAMINA, the work under development
and expected results. The last section contains discussion and conclusions
2. Review of sensitivity analysis methods
A PA model typically involves several hundred input parameters, an important fraction of whom
are uncertain, thus a joint probability density function is needed to characterise their uncertainty and
the possible dependence structure among them. If all inputs are independent, the individual (marginal)
probability density functions (pdfs) are enough in order to characterise such uncertainty. The
use of the Monte Carlo method allows mapping the input space onto the output variable space and
estimate consequences.
In addition to characterising as accurately as possible the consequences associated to a repository,
which is the target of an uncertainty analysis, identifying the most relevant input parameters, whatever
this means, is a key task in a PA. A real problem arises when we ask for ‘relevant’ or ‘important’
input parameters: the interpretation of these words; what means ‘relevant’, ‘important’ and
similar words? An input parameter can be considered important with respect to a given output variable
if a strong correlation exists between both (linear relation), but it could also be considered so if
the output takes remarkably high values when the input takes values in a given region, or if that input
contributes a large fraction of the output variance (considered as a measure of uncertainty).
Another issue that arises in the SA area is the study of interactions. We say that two input parameters
interact when the joint effect of both is different from the addition of their individual effects
(interactions of order 2). This concept is naturally extended to any number of input factors. In general,
main effects (individual effects of each input parameter) are more important than second order
interactions, second are more important than third order interactions and so on, though this is not
always true. Interactions deserve to be studied in order to know the true structure of the system
model under study. Not all SA techniques are able to study interactions and in some cases, though
they are able, the study could be impractical due to different reasons (extreme computational cost,
too large diversity of possibilities, etc.)
The existence of different interpretations of importance have triggered the development, over the
last twenty-five to thirty years, of a variety of SA methods designed to study the model from different
points of view, each one developed according to each given interpretation. Nowadays a large
corpus is available to the SA practitioner, who may choose appropriate methods to perform a specific
type of SA attending to his/her interests and needs. PAMINA pays special attention to screening
and global methods, which are further explained in the next sections.
388