2016/11/25 by Gregory Beylkin, Beylkin, Gregory, Lucas Monzón +3
Biochemistry, Genetics and Molecular Biology · Chemistry · #FOS: Mathematics #Gene expression and cancer classification #Numerical Analysis (math.NA) #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.1611.08580
openalex publication_date 2016/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new approximate multiresolution analysis (MRA) using a single\nGaussian as the scaling function, which we call Gaussian MRA (GMRA). As an\ninitial application, we employ this new tool to accurately and efficiently\ncompute the probability density function (PDF) of the product of independent\nrandom variables. In contrast with Monte-Carlo (MC) type methods (the only\nother universal approach known to address this problem), our method not only\nachieves accuracies beyond the reach of MC but also produces a PDF expressed as\na Gaussian mixture, thus allowing for further efficient computations. We also\nshow that an exact MRA corresponding to our GMRA can be constructed for a\nmatching user-selected accuracy.\n