Inverse problems as statistics

By Philip B. Stark. 2002

253 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/42c4fd5c7e45b31651b8cee4adc3ad8b6bcf4d87

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

In Environmental Engineering

Citations in the corpus

Recent advances in diffuse optical imaging (2005, methodology): “…(10) is equivalent to minimizing its negative logarithm, which is (8), but can offer further approaches which deal with prior information and covariance estimates in a direct and intuitive manner (Kwee 1999, Kohlemainen 2001, Mosegaard and Sambridge 2002, Evans and Stark 2002, Oh et al 2002).”
Bayesian Recovery of the Initial Condition for the Heat Equation (2011, background): “This heat conduction inverse problem has been studied in frequentist literature (see, e.g., Bissantz and Holzmann, 2008; Cavalier, 2008, 2011; Golubev and Khas′minskĭı, 1999; Mair, 1994; Mair and Ruymgaart, 1996) and has also been addressed in Bayesian framework (with additional assumptions on the…”
Solving inverse problems using data-driven models (2019, methodology): “Our brief survey in Sections 3.1, 3.2.1 and 3.2.2 is based on the excellent survey papers by Evans and Stark (2002), Stuart (2010) and Dashti and Stuart (2017).”
Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise (2004, background): “Whereas there exists a huge literature on linear inverse problems with random noise (see [8] for a recent review), only a few results have been published on nonlinear problems of this kind (see e.”
Stochastic spectral methods for efficient Bayesian solution of inverse problems (2005, background): “Inverse problems, broadly defined, arise from indirect observations of a quantity of interest [1,2].”
Discretization-invariant Bayesian inversion and Besov space priors (2009, unknown): “For general reference on Bayesian inversion see [33, 48, 27, 63, 13].”
Periodic boxcar deconvolution and diophantine approximation (2004, background): “There is a large literature on statistical inverse problems—for some recent reviews see Tenorio (2001) and Evans and Stark (2002).”
A stochastic collocation approach to Bayesian inference in inverse problems (2009, background): “The Bayesian approach to inverse problems [6,13,18,22,23] provides a foundation for inference from noisy and incomplete data, a natural mechanism for incorporating physical constraints and heterogeneous sources of information, and a quantitative assessment of uncertainty in the inverse solution.”
Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems (2018, unknown): “, multi-ﬁdelity polynomial chaos, surrogate modeling, Markov chain Monte Carlo 1. Introduction. Inverse problems are found in many applications, such as heat transfer, geophysics, and medical imaging [10, 17]. One of the central questions in inverse problems is to estimate the unknown parameters or ”
Two estimators of the mean of a counting process with panel count data (2000, methodology): “…differs from the NPMLE of F studied by Groeneboom (1991), Groeneboom and Wellner (1992), Wellner (1995) and Groeneboom (1996), and is somewhat inefficient, even under the “separation type” hypotheses under which the NPMLE ̂n t converges to F t at rate n1/3; cf. Wellner (1995) and Groeneboom (1996).”
Bilevel approaches for learning of variational imaging models (2015, methodology): “…and statistics (in particular signal processing) using ﬁlters [60, 73, 28] and multi scale analysis [79, 50, 80], in statistical inverse problems using Bayesian inversion and machine learning [37] and in mathematical analysis using variational calculus, PDEs and numerical optimisation [71].”
Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems (2015, background): “In these applications the goal is to estimate some unknown model parameters or inputs from indirect observations [14, 21].”
A sequential Monte Carlo approach for marine ecological prediction (2006, background): “Evans and Stark (2002) point out, however, that such inverse approaches have a strong parallel in statistical estimation.”
Estimation of a convex function: characterizations and asymptotic theory. (2001, unknown): “By Lemma 4.1 in Groeneboom (1996), we get that, for each τ >0, MMR 1 nnTT nnτ ≥ 1 4 Tf τ/n −Tf 0 1−H 2 f τ/n f 0 2n so that liminf n→∞ n r MMR 1 nnTT nnτ ≥ 1 4 cτ r e”