Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems
Abstract
Normalized differences of several adjacent observations, referred to as pseudo-measurement errors in this paper, are used in so-called difference-based estimation methods as building blocks for the variance estimate of measurement errors. Numerical results demonstrate that pseudo-measurement errors can be used to serve the role of measurement errors. Based on this information, we propose the use of pseudo-measurement errors to determine an appropriate statistical model and then to subsequently investigate whether there is a mathematical model misspecification or error. We also propose to use the information provided by pseudo-measurement errors to quantify uncertainty in parameter estimation by bootstrapping methods. A number of numerical examples are given to illustrate the effectiveness of these proposed methods.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 07, 2016
- Source ID
- 10.1515/jiip-2015-0090
Entities
People
- H. Thomas Banks
- Jared Catenacci
- Shuhua Hu
Organizations
- Air Force Office of Scientific Research
- North Carolina State University