On computing distributions of products of random variables via Gaussian multiresolution analysis
Provides a new analytical tool for computing product distributions, which is a fundamental problem in probability and statistics, but the method is domain-specific and incremental.
The authors introduce a Gaussian multiresolution analysis (GMRA) to compute the PDF of products of independent random variables, achieving higher accuracy than Monte Carlo methods and producing a Gaussian mixture representation.
We introduce a new approximate multiresolution analysis (MRA) using a single Gaussian as the scaling function, which we call Gaussian MRA (GMRA). As an initial application, we employ this new tool to accurately and efficiently compute the probability density function (PDF) of the product of independent random variables. In contrast with Monte-Carlo (MC) type methods (the only other universal approach known to address this problem), our method not only achieves accuracies beyond the reach of MC but also produces a PDF expressed as a Gaussian mixture, thus allowing for further efficient computations. We also show that an exact MRA corresponding to our GMRA can be constructed for a matching user-selected accuracy.