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

被引：1
|
作者：
Bourgey, Florian [1 ,2 ]
Gobet, Emmanuel [3 ]
Rey, Clement [3 ]
机构：
[1] Ecole Polytech, Inst Polytech Paris, Ctr Math Appl CMAP, CNRS, Route DE Saclay, F-91128 Palaiseau, France
[2] Bloomberg LP, Quantitat Res, 3 Queen Victoria St, London EC4N 4TQ, England
[3] Ecole Polytech, CMAP, F-91120 Palaiseau, France
来源：
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION | 2022年 / 10卷 / 04期
关键词：
metamodeling; orthogonal polynomials; polynomial chaos expansion; CONVERGENCE;
D O I：
10.1137/21M1413146
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We propose a thorough comparison of polynomial chaos expansion (PCE) for indicator functions of the form 1c <= X for some threshold parameter c is an element of 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.
引用
收藏
页码：1350 / 1383
页数：34
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