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

Autor:	Harvey Thomas Banks, Jared Catenacci, Shuhua Hu
Rok vydání:	2016
Předmět:	Observational error Estimation theory Applied Mathematics Statistical model Variance (accounting) Inverse problem 01 natural sciences 010101 applied mathematics 010104 statistics & probability Statistics 0101 mathematics Estimation methods Algorithm Bootstrapping (statistics) Mathematics
Zdroj:	Journal of Inverse and Ill-posed Problems. 24:413-433
ISSN:	1569-3945 0928-0219
DOI:	10.1515/jiip-2015-0090
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::af8f16ba027be3d8fec7d9506fd4ea14 https://doi.org/10.1515/jiip-2015-0090 Zobrazit plný text záznamu