A Comparative Study of Polynomial-Type Chaos Expansions for Indicator Functions

Florian Bourgey; Emmanuel Gobet; Clément Rey

doi:10.1137/21M1413146

A Comparative Study of Polynomial-Type Chaos Expansions for Indicator Functions

Florian Bourgey
, Emmanuel Gobet
, Clément Rey

Research output: Contribution to journal › Article › peer-review

Abstract

We propose a thorough comparison of polynomial chaos expansion (PCE) for indicator functions of the form 1_c≤_X for some threshold parameter c ∈ R and a random variable X associated with classical orthogonal polynomials. We provide tight global and localized L² estimates for the resulting truncation of the PCE, and numerical experiments support the tightness of the error estimates. We also compare the theoretical and numerical accuracy of PCE when extra quantile/probability transforms are applied, revealing different optimal choices according to the value of c in the center and the tails of the distribution of X.

Original language	English
Pages (from-to)	1350-1383
Number of pages	34
Journal	SIAM-ASA Journal on Uncertainty Quantification
Volume	10
Issue number	4
DOIs	https://doi.org/10.1137/21M1413146
Publication status	Published - 1 Jan 2022

Keywords

metamodeling
orthogonal polynomials
polynomial chaos expansion

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10.1137/21M1413146

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title = "A Comparative Study of Polynomial-Type Chaos Expansions for Indicator Functions",

abstract = "We propose a thorough comparison of polynomial chaos expansion (PCE) for indicator functions of the form 1c≤X for some threshold parameter c ∈ R and a random variable X associated with classical orthogonal polynomials. We provide tight global and localized L2 estimates for the resulting truncation of the PCE, and numerical experiments support the tightness of the error estimates. We also compare the theoretical and numerical accuracy of PCE when extra quantile/probability transforms are applied, revealing different optimal choices according to the value of c in the center and the tails of the distribution of X.",

keywords = "metamodeling, orthogonal polynomials, polynomial chaos expansion",

author = "Florian Bourgey and Emmanuel Gobet and Cl{\'e}ment Rey",

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AU - Bourgey, Florian

AU - Gobet, Emmanuel

AU - Rey, Clément

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Y1 - 2022/1/1

N2 - We propose a thorough comparison of polynomial chaos expansion (PCE) for indicator functions of the form 1c≤X for some threshold parameter c ∈ R and a random variable X associated with classical orthogonal polynomials. We provide tight global and localized L2 estimates for the resulting truncation of the PCE, and numerical experiments support the tightness of the error estimates. We also compare the theoretical and numerical accuracy of PCE when extra quantile/probability transforms are applied, revealing different optimal choices according to the value of c in the center and the tails of the distribution of X.

AB - We propose a thorough comparison of polynomial chaos expansion (PCE) for indicator functions of the form 1c≤X for some threshold parameter c ∈ R and a random variable X associated with classical orthogonal polynomials. We provide tight global and localized L2 estimates for the resulting truncation of the PCE, and numerical experiments support the tightness of the error estimates. We also compare the theoretical and numerical accuracy of PCE when extra quantile/probability transforms are applied, revealing different optimal choices according to the value of c in the center and the tails of the distribution of X.

KW - metamodeling

KW - orthogonal polynomials

KW - polynomial chaos expansion

UR - https://www.scopus.com/pages/publications/85145441981

U2 - 10.1137/21M1413146

DO - 10.1137/21M1413146

M3 - Article

AN - SCOPUS:85145441981

SN - 2166-2525

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EP - 1383

JO - SIAM-ASA Journal on Uncertainty Quantification

JF - SIAM-ASA Journal on Uncertainty Quantification

IS - 4

ER -

A Comparative Study of Polynomial-Type Chaos Expansions for Indicator Functions

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Keywords

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