An Inverse Problem Statistical Methodology Summary

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 12, 2008
Accession Number
ADA477302

Entities

People

  • H. Thomas Banks
  • J. R. Samuels Jr.
  • Karyn L. Sutton
  • M. Davidian

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Computational Science
  • Computations
  • Data Science
  • Differential Equations
  • Equations
  • Estimators
  • Experimental Design
  • Information Science
  • Inverse Problems
  • Mathematical Models
  • Models
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Linear Algebra
  • Regression Analysis.