Statistical and Computational Inverse Problems

By F. Liang, Jianhua Huang. Technometrics, 2006

1,673 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4edb0aa5f6ee8268f6b278858005c0e6e9127120

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Citations in the corpus

Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering (2013, background): “For example, in electrical impedance tomography (EIT) problems [4] we try to reconstruct the resistance ﬁeld of a body based on voltages induced by injected currents.”
Filtering Complex Turbulent Systems (2012, methodology): “In the second direction, Bayesian hierarchical modeling [17] and reduced order filtering strategies [109, 56, 128, 8, 9, 25, 42, 43, 114, 70, 63] based on the Kalman filter [7, 27, 74] have been developed with some success in these extremely complex high dimensional nonlinear systems.”
Learning from Examples as an Inverse Problem (2005, positive): “Statistical methods were recently applied in the context of inverse problems (Kaipio and Somersalo, 2005).”
On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems (2007, background): “Examples of such applications ar e GPS and inertial navigation [5], [6], target tracking [7]–[ 9], estimation of biological processes [10], telecommunicati ons [11], [12], stochastic optimal control [13], [14] and inver s problems in physics [15].”
Computer Model Calibration Using High-Dimensional Output (2008, methodology): “When the simulation code is sufﬁciently fast, estimation approaches based on Monte Carlo can be used (Berliner 2001; Higdon, Lee, and Holloman 2003; Kaipio and Somersalo 2004).”
Stochastic spectral methods for efficient Bayesian solution of inverse problems (2005, background): “Furthermore, as highlighted in [2], inverse problems are often non-local and/or non-causal.”
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion (2012, methodology): “The Bayesian approach does this by reformulating the inverse problem as a problem in statistical inference, incorporating uncertainties in the measurements, the forward model, and prior information on the parameters [27, 43].”
Calderon's inverse conductivity problem in the plane (2006, background): “One may find a review for medical applications in [13]; for statistical methods in electrical impedance tomography see [17].”
Bayesian inference with optimal maps (2011, background): “This discrepancy ensures that we do not commit an “inverse crime” [3].”
Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems (2015, methodology): “The Bayesian approach [21, 34, 35] does this by reformulating the inverse problem as a problem in statistical inference, incorporating uncertainties in the observations and prior information on the parameters.”
Bayesian Filtering and Smoothing (2013, methodology): “Physical systems which are time-varying and measured through nonideal sensors can sometimes be formulated as stochastic state space models, and the time evolution of the system can be estimated using optimal filters (Kaipio and Somersalo, 2005).”
A unified framework for multilevel uncertainty quantification in Bayesian inverse problems (2016, background): “Classical or simple Bayesian inversion is concerned with the estimation of fixed yet unknown parameters m of the physical simulator [3, 4].”
An ensemble Kalman filtering approach to highway traffic estimation using GPS enabled mobile devices (2008, background): “For more information on modeling errors and state noise covariance estimation, see for example [28], [29].”
Machine learning of linear differential equations using Gaussian processes (2017, background): “This setup defines a broad class of problems that are often referred to as “inverse problems” (see [20,46]) and they permeate applications across a wide range of scientific disciplines.”