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

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.

Automated summary

This article proposes a comprehensive comparison of polynomial chaos expansion (PCE) for indicator functions, providing tight estimates for the resulting truncation of PCE and analyzing the theoretical and numerical accuracy when extra transforms are applied. Different optimal choices are revealed based on the value of the threshold parameter.