Statistical inverse problems: discretization, model reduction and inverse crimes

By Jari P. Kaipio, E. Somersalo. 2007

559 citations recorded by the source corpus.

Subfields: Applied Mathematics, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c9b363e30a248c059c62518f92183eb1f462c81

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In Applied Mathematics

In Electrical and Electronic Engineering

In Mathematical Physics

Citations in the corpus

Solving inverse problems using data-driven models (2019, methodology): “…particular has led to the advance of methods that incorporate information about the structure of the parameters to be determined in terms of sparsity assumptions (Daubechies, Defrise and De Mol 2004, Jin and Maass 2012b) or stochastic models (Kaipio and Somersalo 2007, Mueller and Siltanen 2012).”
Bayesian Solution Uncertainty Quantification for Differential Equations (2013, methodology): “We use of the mathematical framework for deﬁning numerical problems on function spaces developed through the work of Stuart (2010), Kaipio and Somersalo (2007), O’Hagan (1992), and Skilling (1991).”
An ensemble Kalman filtering approach to highway traffic estimation using GPS enabled mobile devices (2008, methodology): “The construction of a smooth prior is made using a framework proposed in [35].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “The work [110, 111] can be seen as dealing with”
Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion (2013, methodology): “[7] The second strategy uses the gPC-based surrogate model derived following Xiu [2007] within a two-stage MCMC simulation scheme [e.g., Liu, 2001; Christen and Fox, 2005; Efendiev et al., 2005; Kaipio and Somersalo, 2007; Mondal et al., 2010; Cui et al., 2011], using DREAM ZSð Þ.”
Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA) (2014, background): “Such problems are ill posed, i.e., the solution is nonunique or too sensitive to data, and subject to uncertainty, thus they are commonly evaluated within a statistical framework [McLaughlin and Townley, 1996; Carrera et al., 2005; Oliver et al., 2008; Kaipio and Somersalo, 2007].”
Bayesian inverse problems for functions and applications to fluid mechanics (2009, methodology): “to first discretize the problem and then apply the Bayesian methodology to a finite-dimensional problem; the idea of trying to capture the limit of infinite resolution is addressed by use of statistical extrapolation techniques based on modelling the error from finite-dimensional approximation [41].”
Inverse problems: A Bayesian perspective (2010, methodology): “The idea concluding the proof of the first part of Theorem 5.4 is standard in the theory of calculus of variations: see Dacarogna (1989, Chapter 3, Theorem 1.1).”