Sensitivity Analysis for Stochastic Simulators Using Differential Entropy

Azzi, Soumaya; Sudret, Bruno; Wiart, Joe

doi:10.1615/int.j.uncertaintyquantification.2020031610

Cited by 9 publications

(18 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Denote by MRE(T, m) the MRE based on T number of calls and m repetitions, so that the number of explorations is T /(p+1)/m. To shorten the notation, let (X (1) , X (1) ) = X, f (X (1) , Z…”

Section: Example 4 Returns To the Model (21)mentioning

confidence: 99%

“…Lemma D.2 (Moments of order 2). The moments of order 2 are given by E ξ (UL)2 j;m1 = Var E X f (X (1) , Z (1,1) )f ( X(1) −j , Z…”

Section: G Mazomentioning

confidence: 99%

“…E f (X (1) , Z (1,1) )f (X (1) , Z (1,2) )f (X (1) , Z (1,3) )f (X (1) , Z (1,4) ) 1) , Z (1,1) ) 2 f (X (1) , Z (1,2) )f (X (1) , Z (1,3) ) 1) , Z (1,1) ) 3 f (X (1) , Z (1,2) ) + m m 4 E f (X (1) , Z (1,1) ) 4 E f (X (1) , Z (1,1) ) 2 f (X (1) , Z (1,2) ) 2…”

Section: G Mazomentioning

confidence: 99%

“…The first contains the m 2 (m − 1) 2 terms that satisfy k 1 = k 2 and k 3 = k 4 . In this part, all the terms are equal to E E X f (X (1) , Z (1,1) )f ( X(1) −j , Z…”

Section: G Mazomentioning

confidence: 99%

“…The estimates are then averaged over ω to make the final sensitivity estimates. In [1], to the best of my understanding, the stochastic model is represented as a deterministic mapping which with an input associates a probability density function. The Sobol-Hoeffding decomposition is applied to the mapping which with an input associates the entropy of the output evaluated at that input.…”

mentioning

confidence: 99%

See 4 more Smart Citations

A Trade-Off Between Explorations and Repetitions for Estimators of Two Global Sensitivity Indices in Stochastic Models Induced by Probability Measures

Mazo¹

2021

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

Sobol sensitivity indices assess how the output of a given mathematical model is sensitive to its inputs. If the model is stochastic then it cannot be represented as a function of the inputs, thus raising questions as how to do a sensitivity analysis in those models. Practitioners have been using a method that exploits the availability of softwares for deterministic models. For each input, the stochastic model is repeated and the outputs are averaged. These averages are seen as if they came from a deterministic model and hence Sobol's method can be used. However, in the context of limited computational resources, one must ensure that the number of repetitions of the stochastic model multiplied by the number of explorations of the input space is less than a fixed threshold. The problem of finding an optimal tradeoff between the repetitions and the explorations is addressed. A bound on an error criterion that penalizes bad rankings of the inputs' sensitivities is minimized. The estimator induced by the empirical method described above is shown to be asymptotically biased if the number of repetitions goes to infinity too slowly. A functional relationship between the output, the input and some random noise is derived from minimal distributional assumptions, which leads to a new sensitivity index with better statistical properties. The theory is illustrated on numerical experiments.

show abstract

“…Denote by MRE(T, m) the MRE based on T number of calls and m repetitions, so that the number of explorations is T /(p+1)/m. To shorten the notation, let (X (1) , X (1) ) = X, f (X (1) , Z…”

Section: Example 4 Returns To the Model (21)mentioning

confidence: 99%

“…Lemma D.2 (Moments of order 2). The moments of order 2 are given by E ξ (UL)2 j;m1 = Var E X f (X (1) , Z (1,1) )f ( X(1) −j , Z…”

Section: G Mazomentioning

confidence: 99%

Section: G Mazomentioning

confidence: 99%

“…The first contains the m 2 (m − 1) 2 terms that satisfy k 1 = k 2 and k 3 = k 4 . In this part, all the terms are equal to E E X f (X (1) , Z (1,1) )f ( X(1) −j , Z…”

Section: G Mazomentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations