1,307 research outputs found
Derivative based global sensitivity measures
The method of derivative based global sensitivity measures (DGSM) has
recently become popular among practitioners. It has a strong link with the
Morris screening method and Sobol' sensitivity indices and has several
advantages over them. DGSM are very easy to implement and evaluate numerically.
The computational time required for numerical evaluation of DGSM is generally
much lower than that for estimation of Sobol' sensitivity indices. This paper
presents a survey of recent advances in DGSM concerning lower and upper bounds
on the values of Sobol' total sensitivity indices . Using these
bounds it is possible in most cases to get a good practical estimation of the
values of . Several examples are used to illustrate an
application of DGSM
Derivative-based global sensitivity measures: general links with Sobol' indices and numerical tests
The estimation of variance-based importance measures (called Sobol' indices)
of the input variables of a numerical model can require a large number of model
evaluations. It turns to be unacceptable for high-dimensional model involving a
large number of input variables (typically more than ten). Recently, Sobol and
Kucherenko have proposed the Derivative-based Global Sensitivity Measures
(DGSM), defined as the integral of the squared derivatives of the model output,
showing that it can help to solve the problem of dimensionality in some cases.
We provide a general inequality link between DGSM and total Sobol' indices for
input variables belonging to the class of Boltzmann probability measures, thus
extending the previous results of Sobol and Kucherenko for uniform and normal
measures. The special case of log-concave measures is also described. This link
provides a DGSM-based maximal bound for the total Sobol indices. Numerical
tests show the performance of the bound and its usefulness in practice
Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models
Global sensitivity analysis aims at quantifying the impact of input
variability onto the variation of the response of a computational model. It has
been widely applied to deterministic simulators, for which a set of input
parameters has a unique corresponding output value. Stochastic simulators,
however, have intrinsic randomness due to their use of (pseudo)random numbers,
so they give different results when run twice with the same input parameters
but non-common random numbers. Due to this random nature, conventional Sobol'
indices, used in global sensitivity analysis, can be extended to stochastic
simulators in different ways. In this paper, we discuss three possible
extensions and focus on those that depend only on the statistical dependence
between input and output. This choice ignores the detailed data generating
process involving the internal randomness, and can thus be applied to a wider
class of problems. We propose to use the generalized lambda model to emulate
the response distribution of stochastic simulators. Such a surrogate can be
constructed without the need for replications. The proposed method is applied
to three examples including two case studies in finance and epidemiology. The
results confirm the convergence of the approach for estimating the sensitivity
indices even with the presence of strong heteroskedasticity and small
signal-to-noise ratio
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