Data-based Automatic Discretization of Nonparametric Distributions

When I wrote a series of my discretization papers (Tanaka & Toda, 2013, 2015; Farmer & Toda, 2017), I didn’t know much about numerical integration. In 2017, I taught numerical methods to Ph.D. students and studied quadrature methods myself. I realized that the Golub-Welsch algorithm of Gaussian quadrature requires only inputting the moments of the probability distribution, so I thought I can feed in sample moments to discretize a nonparametric distribution from data. The idea was not a big deal, so after some procrastination I wrote up the paper in a few days in May 2018.