A new method for estimating Sobol’ indices is proposed. The new method makes use of 3 independent input vectors rather than the usual 2. It attains much greater accuracy on problems where the target Sobol’ index is small, even outperforming some oracles which adjust using the true but unknown mean of the function. When the target Sobol’ index is quite large, the oracles do better than the new m...

Sensitivity analysis has been widely used for rational decision making of energy retrofit alternatives. A Sobol method is a variance based approach and provides powerful post-processing sensitivity results that enable to quantitatively identify influential and non-influential inputs. It can account for impacts of each input as well as impacts caused by all possible interactions between each inp...

This study presents improved understanding of sensitivity analysis methods through a comparison of the local sensitivity and two global sensitivity analysis methods: the Morris and Sobol′/Saltelli methods. We re-interpret the variance-based sensitivity indices from the Sobol′/Saltelli method as difference-based measures. It suggests that the difference-based local and Morris methods provide the...

Monte Carlo simulation is widely used to price complex nancial instruments. Recent theoretical results and extensive computer testing indicate that deterministic methods may be far superior in speed and conndence. Simulations using the Sobol or Faure points are examples of deterministic methods. For the sake of brevity, we refer to a deterministic method using the name of the sequence of points...

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 fo...

Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to use a reduced model (metamodel) to perform sensitivity analysis, whose outputs are numerically close to the ones of the original model, while being much fas...

A novel theoretical and numerical framework for the estimation of Sobol ’ sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical methods, namely the quadrature integration method which may be very efficient for problems of low dimensionality and the MC/QMC estimators based on the acceptanc...

This paper applies the Sobol’ decomposition of a function of many random variables to a problem in structural mechanics, namely the collapse of a two story two bay frame under gravity load. Prior to introduction of this example application, the Sobol’ decomposition itself is reviewed and extended to cover the case in which the input random variables have Gaussian distribution. Then, an illustra...

A novel approach for estimation variance based sensitivity indices for models with dependent variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobol’ sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobol’ formulas are derived. A copula based approach is proposed for sampling from arbitrary multivariate proba...

Global sensitivity analysis is widely used in many areas of science, biology, sociology and policy planning. The variance-based methods also known as Sobol' sensitivity indices has become the method of choice among practitioners due to its efficiency and ease of interpretation. For complex practical problems, estimation of Sobol' sensitivity indices generally requires a large number of function...