Plutonium Biokinetics in Human Body A. Luciani - Kit-Bibliothek - FZK

The use of such values allows to characterize the uncertainty of the output variable by two
numbers.
In comparison to other uncertainty analysis techniques [169] (such as Taylor series
based differential analysis, response surface methodology or Fourier amplitude test), Monte
Carlo procedures have some important advantages:
• The full range of each input variable is sampled and then used as input for calculating
model predictions;
• The uncertainty is evaluated without using surrogate models, i.e. an approximating model
that resembles the original model under study and on which the uncertainty analysis can
be performed more effectively;
• The full stratification over the range of each input variable facilitates the identification of
non-linearities, thresholds and discontinuities;
• The approach is conceptually simple and can be easily implemented in iterative
procedures.
The most relevant drawback of using Monte Carlo techniques for uncertainty analyses
is the fact that a large number of model evaluations are required. Therefore if the model is
computationally expensive to evaluate or many input variables are considered and for each
variable many values are sampled, the time and cost for performing the required calculations
may be too large. In this context results of the above sensitivity analysis can be used for
screening purposes in order to reduce the number of input variables that are considered in the
uncertainty analysis [170]. Only those input variables that significantly affect model
predictions for a certain output variable should be considered. Furthermore computational
time and cost needs for uncertainty analysis can be reduced by adopting an effective
procedure for the generation of the random values of the input variables. The Latin Hypercube
Sampling (LHS) procedure [170] rather than random sampling techniques will improve the
efficiency of random values generation. The LHS procedure is a stratified sampling technique
that generates a sample of size m for each of the n input parameters in the following way:
• The range of each input variable is divided into m non-overlapping intervals on the basis
of equal probability. Such a division will therefore depend on the statistical distribution
assumed for the input variable;
• One value from each interval is randomly generated according to the statistical
distribution in this interval;
• The previous two steps are repeated for each of the n input variables;
• The m values obtained for the x 1 input variable are paired in random manner with the m
values of the x 2 input variable. These m pairs are combined in a random manner with the
m values of the x 3 input variable and so on until all the n input variables are considered.
The main advantage of the LHS procedure is that the full range of input parameters is
sampled, whereas in a simple random sampling scheme, combinations of input parameter
values could easily come from the same subintervals.
In adopting the LHS procedure the choice of the sample size m should be carefully considered
in relation to the number n of input variables. It is preferable that m (the size of the sample,
i.e. the number of values sampled for each input variable) be greater than or equal to (4/3)•n
[171]. Of course, if the model is simple and can be run quickly , then m could even be larger.
The sensitivity analysis has already pointed out the main significant transfer rates for
the urinary excretion, fecal excretion and blood content of Plutonium predicted by the
optimized model (Model-b). These parameters represent the input variables of the uncertainty
analysis. In accordance with similar recent studies [166] a log-normal distribution for the
input variable was assumed. The range of variation of the transfer rates was set at the 1 st and
99 th percentile of the log-normal distribution centred around the base case values.
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