{"title":"A Comparative Study of Polynomial-Type Chaos Expansions for Indicator Functions","authors":"Florian Bourgey, E. Gobet, C. Rey","doi":"10.1137/21m1413146","DOIUrl":null,"url":null,"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 L 2 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 .","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":"32 1","pages":"1350-1383"},"PeriodicalIF":2.1000,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siam-Asa Journal on Uncertainty Quantification","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1137/21m1413146","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 2
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 L 2 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 .
期刊介绍：
SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.
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