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 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 .