Can Sobol Indices Be Negative If you calculate Sobol indices negative values shouldn t arise unless you didn t use a sufficient sample size
As Christoph explained in theory the indices cannot be negative However it happens for numerical reasons Before I go into details make sure you have enough samples Negative Sobol values are due to numerical errors Increasing the number of points n should help The number of sample required to have a good analysis increases with the dimensionality of the problem e g for a 3 dimension
Can Sobol Indices Be Negative
Can Sobol Indices Be Negative
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Variance based sensitivity analysis often referred to as the Sobol method or Sobol indices after Ilya M Sobol is a form of global sensitivity analysis Working within a probabilistic framework it decomposes the variance of the output of the model or system into fractions which can be attributed to inputs or sets of inputs For example given a model with two inputs and one output one might find that 70 of the output variance is caused by the variance in the first input 20 b A negative Sobol index can appear when you compute the Sobol indices by Monte Carlo and don t use enough samples see also the first few posts by damarginal in this
Should it ever be negative What if support of xj depends on xk E g input space has holes Computational New work from Song Nelson Staum 2015 using Shapley value looks super I am using variance based sensitivity analysis method from SAFE toolbox in matlab to determine the first order Si and total order sensitivity indices STi Theoretically the STi is either equal
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It can be disconcerting to obtain estimates that are negative or above one which are not possible values for the true indices This is relatively infrequent when using method D In the sequel we focus on the estimation of variance based sensitivity indices also called Sobol indices Sobol 1993 As eluded previously a Monte Carlo sample is required to
The Sobol indices belong to a specific category of Sensitivity Analysis called Global Sensitivity Analysis GSA GSA computes sensitivity indices by taking into account for Total Sobol indices is a viable alternative the total index for a given input x i represent the effect of all the group of variables that contain x i Hence the difference between the total
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If you calculate Sobol indices negative values shouldn t arise unless you didn t use a sufficient sample size
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As Christoph explained in theory the indices cannot be negative However it happens for numerical reasons Before I go into details make sure you have enough samples
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Can Sobol Indices Be Negative - I am using variance based sensitivity analysis method from SAFE toolbox in matlab to determine the first order Si and total order sensitivity indices STi Theoretically the STi is either equal
