ANALYTICAL APPROXIMATION OF EXACT POISSON-LOGNORMAL LIKELIHOOD FUNCTIONS

Abstract

Abstract—

Simple analytical approximations of exact Poisson-lognormal likelihood functions are obtained numerically. The Poisson-lognormal statistical model describes counting measurements with lognormally distributed normalization factors. The analytical expressions for the likelihood function allow maximum likelihood data fitting using nonlinear-least-squares-minimization computer programs. A computer program that converts count data into analytical approximation parameters as described in this note is freely available for downloading from the Los Alamos Bayesian Web site (www.lanl.gov/bayesian).