Data analysis tools for uncertainty quantification of inverse problems

被引：21

作者：

Tenorio, L. ^{[1
]}

Andersson, F. ^{[2
]}

de Hoop, M. ^{[3
]}

Ma, P. ^{[4
]}

机构：

[1] Colorado Sch Mines, Dept Math & Comp Sci, Golden, CO 80401 USA

[2] Lund Univ, Ctr Math Sci, Lund, Sweden

[3] Purdue Univ, Ctr Computat & Appl Math, W Lafayette, IN 47907 USA

[4] Univ Illinois, Dept Stat, Urbana, IL 61801 USA

来源：

INVERSE PROBLEMS | 2011年 / 27卷 / 04期

基金：

美国国家科学基金会;

关键词：

REGULARIZATION; VARIANCE; ESTIMATORS; MATRIX; SCALE;

D O I：

10.1088/0266-5611/27/4/045001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present exploratory data analysis methods to assess inversion estimates using examples based on l(2)- and l(1)-regularization. These methods can be used to reveal the presence of systematic errors such as bias and discretization effects, or to validate assumptions made on the statistical model used in the analysis. The methods include bounds on the performance of randomized estimators of a large matrix, confidence intervals and bounds for the bias, resampling methods for model validation and construction of training sets of functions with controlled local regularity.

引用

页数：22

共 50 条

[1] Uncertainty quantification in Bayesian inverse problems with model and data dimension reduction
Grana, Dario
de Figueiredo, Leandro Passos
Azevedo, Leonardo
GEOPHYSICS, 2019, 84 (06) : M15 - M24
[2] Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems
Tachella, Julian
Pereyra, Marcelo
INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 238, 2024, 238
[3] An MCMC method for uncertainty quantification in nonnegativity constrained inverse problems
Bardsley, Johnathan M.
Fox, Colin
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2012, 20 (04) : 477 - 498
[4] A unified framework for multilevel uncertainty quantification in Bayesian inverse problems
Nagel, Joseph B.
Sudret, Bruno
PROBABILISTIC ENGINEERING MECHANICS, 2016, 43 : 68 - 84
[5] Uncertainty Quantification in Inverse Scattering Problems With Bayesian Convolutional Neural Networks
Wei, Zhun
Chen, Xudong
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2021, 69 (06) : 3409 - 3418
[6] Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes
Malinverno, A
Briggs, VA
GEOPHYSICS, 2004, 69 (04) : 1005 - 1016
[7] On inverse fuzzy arithmetical problems in uncertainty analysis
Hose, D.
Hanss, M.
PROCEEDINGS OF INTERNATIONAL CONFERENCE ON NOISE AND VIBRATION ENGINEERING (ISMA2018) / INTERNATIONAL CONFERENCE ON UNCERTAINTY IN STRUCTURAL DYNAMICS (USD2018), 2018, : 5143 - 5156
[8] Data Adequacy by an Extended Analytic Hierarchy Process for Inverse Uncertainty Quantification in Nuclear Safety Analysis
Di Maio, Francesco
Coscia, Thomas Matteo
Zio, Enrico
NUCLEAR ENGINEERING AND DESIGN, 2024, 419
[9] Subspace-based Inverse Uncertainty Quantification for Nuclear Data Assessment
Khuwaileh, B. A.
Abdel-Khalik, H. S.
NUCLEAR DATA SHEETS, 2015, 123 : 57 - 61
[10] A multivariate interval approach for inverse uncertainty quantification with limited experimental data
Faes, Matthias
Broggi, Matteo
Patelli, Edoardo
Govers, Yves
Mottershead, John
Beer, Michael
Moens, David
MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2019, 118 : 534 - 548

← 1 2 3 4 5 →