Moment calculations for piecewise-defined functions: an application to stochastic optimization with coherent risk measures

Borgonovo, Emanuele; Peccati, Lorenzo

doi:10.1007/s10479-008-0504-1

Cited by 5 publications

(2 citation statements)

References 29 publications

(47 reference statements)

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“…Let us now study more closely. The operation | f − g | sets forth the piecewise defined function: ( 63 ) Σ={ω: f (ω) = g (ω)} is the set of points where f = g , Ω + is the set of points where f > g , and Ω − the set of points where f < g . Let us now denote by F and G the cumulative distribution functions associated with f and g , respectively: and .…”

Section: New Properties and A Procedures For Obtaining Moment Indepmentioning

confidence: 99%

Moment Independent Importance Measures: New Results and Analytical Test Cases

2010

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Moment independent methods for the sensitivity analysis of model output are attracting growing attention among both academics and practitioners. However, the lack of benchmarks against which to compare numerical strategies forces one to rely on ad hoc experiments in estimating the sensitivity measures. This article introduces a methodology that allows one to obtain moment independent sensitivity measures analytically. We illustrate the procedure by implementing four test cases with different model structures and model input distributions. Numerical experiments are performed at increasing sample size to check convergence of the sensitivity estimates to the analytical values.

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Section: New Properties and A Procedures For Obtaining Moment Indepmentioning

confidence: 99%

Moment Independent Importance Measures: New Results and Analytical Test Cases

2010

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“…Definition 3 (Borgonovo & Peccati, 2010;Herrera, 2007). Consider a finite partition of the domain ,…”

Section: If and Only If It Satisfies (4)mentioning

confidence: 99%

Interactions and computer experiments

Borgonovo

Plischke

Rabitti

2021

Scandinavian J Statistics

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Identifying interactions and understanding the underlying generating mechanism is essential for interpreting the response of black-box models. We offer a systematic analysis of interaction types and corresponding sources, merging results of the broad statistical literature with findings developed within the computer experiment literature. Piecewise-definiteness emerges a self-standing interaction mechanism, alternative to the presence of interaction terms. We find that the scale of the analysis is essential for interpretation, and that no single method is capable of providing the correct identification of the underlying interaction generating mechanisms; conversely a combined approach involving indicators at difference scales is required. We propose a graphical tool called Mikado plot that exploits the link between interaction indicators at the finite scale and global scales to ease the regional visualization of two-factor interactions. The findings are illustrated via numerical experiments with three well-known computer models of different dimensionality and structure.

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