A Monte Carlo Based Analysis of Optimal Design Criteria

Abstract

Optimal design methods (designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates) for inverse or parameter estimation problems are considered. We compare a recent design criteria SE-optimal design (standard error optimal design) with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; here the standard errors for parameters are computed using the optimal mesh along with Monte Carlo simulations as compared to asymptotic theory based standard errors. We illustrate ideas with two examples: the Verhulst-Pearl logistic population model and the standard harmonic oscillator model.

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Document Details

Document Type
Technical Report
Publication Date
Nov 09, 2011
Accession Number
ADA556942

Entities

People

  • Franz Kappel
  • H. Thomas Banks
  • Kathleen J. Holm

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computational Science
  • Data Science
  • Design Criteria
  • Differential Equations
  • Experimental Design
  • Information Science
  • Mathematics
  • Monte Carlo Method
  • Oscillators
  • Random Variables
  • Regression Analysis
  • Sampling
  • Simulations
  • Statistical Algorithms
  • Statistical Analysis

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.