A Moments-Based Method for Computing Multidimensional Orthogonal Polynomial Bases

Abstract

When trying to create a polynomial fit of a function of random variables, a basis of polynomials is required. The generation of that basis is produced under the constraint that it is orthogonal with respect to the probability distribution function of the random variable inputs. We propose a computational method for producing multidimensional orthogonal polynomial bases for arbitrary, possibly dependent random variables. We will then show that it produces the correct results for the case where the random variables are independent, and demonstrate its utility in the case where the random variables are dependent.