Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems

作者：Banks H Thomas; Catenacci Jared; Hu Shuhua

来源：Journal of Inverse and Ill-Posed Problems, 2016, 24(4): 413-433.

DOI：10.1515/jiip-2015-0090

<jats:title>Abstract</jats:title><jats:p>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.</jats:p>

• 出版日期2016-8