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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 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.
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https://hal.archives-ouvertes.fr/hal-03199734
Contributor : Florian Bourgey <>
Submitted on : Thursday, April 15, 2021 - 10:26:29 PM
Last modification on : Saturday, May 29, 2021 - 7:46:03 PM
Long-term archiving on: : Friday, July 16, 2021 - 7:20:13 PM

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  • HAL Id : hal-03199734, version 1

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Florian Bourgey, , Clément Rey. A comparative study of polynomial-type chaos expansions for indicator functions. 2021. ⟨hal-03199734⟩

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