Statistical and computational inverse problems

By Jari P. Kaipio, E. Somersalo. 2004

1,023 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ae74cdd3c29acc43fcdac76db580e18e8372859b

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Citations in the corpus

Introduction to the Bayesian Approach Applied to Elastic Constants Identification (2010, background): “For additional details on the theory ofBayesian analysis, we also refer the reader to [24,25].”
Bilevel approaches for learning of variational imaging models (2015, background): “Appropriate data fidelity distances d are mostly driven by statistical considerations that model our knowledge of the data distribution [56, 58].”
The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions (2019, methodology): “For completeness, we note that the posterior density p(u|y) can be alternatively obtained from the joint density of p(u, y), see [11, 42].”
A markov random field model of contamination source identification in porous media flow (2006, background): “All equations are solved on a rather fine grid to generate simulation data, thus avoiding the so called ‘inverse crimes’ [16].”
MAP estimators and their consistency in Bayesian nonparametric inverse problems (2013, methodology): “We first note that MAP estimators are widely used in practice in the infinite dimensional context [30, 22].”
Discretization-invariant Bayesian inversion and Besov space priors (2009, unknown): “Z) πU(u) πM(m) (27) du satisﬁes the assumptions of Deﬁnition 3. Compare formulas (23) and (27) and see Appendix C for further discussion. Note that (27) is widely used in practical Bayesian inversion [63, 33, 13]. Stability of the reconstructor with respect to data mis important from the point of vi”
Bayesian inverse problems for functions and applications to fluid mechanics (2009, methodology): “Finding x to maximize the probability μy(dx) is referred to as a MAP estimator in the Bayesian statistics literature [ 39 ].”
Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography (2014, methodology): “[12] for details).”
An alternating iterative procedure for the Cauchy problem for the Helmholtz equation (2014, background): “More examples of ill–posed problems can be found in the literature such as Groetsch [8], Hadamard [9], Isakov [12], Kaipio [13], and Vogel [23].”
Nonparametric statistical inverse problems (2008, background): “Other topics and reviews may be found in [24, 41, 55, 57, 59, 63].”
A Bayesian approach for parameter estimation and prediction using a computationally intensive model (2014, background): “Unlike more standard Bayesian inverse methodologies [4, 5], model calibration approaches must accommodate the high cost of evaluating the computational model; in many cases, only a limited number of model evaluations can be made.”