An Inverse Problem Statistical Methodology Summary

This paper discusses statistical and computational aspects of inverse or parameter estimation problems based on Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) with appropriate corresponding data noise assumptions of constant variance and nonconstant variance (relative error), respectively. Among the topics addressed are mathematical model, statistical model and data assumptions, and some techniques (residual plots, sensitivity analysis, model comparison tests) for verifying these. The ideas are illustrated throughout with the popular logistic growth model of Verhulst and Pearl as well as with a recently developed population-level model of pneumococcal disease spread.
Prepared in cooperation with the Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC and the Department of Mathematics and Statistics, Arizona State University, Tempe, AZ.