Inverse Problems and Imaging (IPI)

Bayesian inverse problems with Monte Carlo forward models
Pages: 81 - 105, Issue 1, February 2013

doi:10.3934/ipi.2013.7.81      Abstract        References        Full text (939.5K)           Related Articles

Guillaume Bal - Department of Applied Physics and Applied Mathematics, Columbia University, 200 S. W. Mudd Building, MC 4701, 500 W. 120th Street, New York, NY 10027, United States (email)
Ian Langmore - Department of Applied Physics and Applied Mathematics, Columbia University, 200 S. W. Mudd Building, MC 4701, 500 W. 120th Street, New York, NY 10027, United States (email)
Youssef Marzouk - Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, United States (email)

1 Simon Arridge, et al., Approximation errors and model reduction with an application in optical diffusion tomography, Inverse Problems, 22 (2006).
2 Guillaume Bal, Anthony Davis and Ian Langmore, A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport, J. Computational Physics, 230 (2011), 7723-7735.
3 George Casella and Robert Berger, "Statistical Inference," Duxbury, 2002.
4 Jin Chen and Xavier Intes, Time-gated perturbation Monte Carlo for whole body functional imaging in small animals, Optics Express, 17 (2009).
5 J. Andrés Christen and Colin Fox, Markov chain Monte Carlo using an approximation, Journal of Computational and Graphical Statistics, 14 (2005), 795-810       
6 Rick Durrett, "Probability: Theory and Examples," third edition, Brooks/Cole, 2005.
7 Yalchin Efendiev, Thomas Hou and W. Luo, Preconditioning Markov chain Monte Carlo simulations using coarse-scale models, SIAM J. Sci. Comput., 28 (2006), 776-803.       
8 Charles J. Geyer, Practical Markov chain Monte Carlo, Statistical Science, 7 (1992), 473-511.
9 Carole K. Hayakawa and Jerome Spanier, Perturbation Monte Carlo methods for the solution of inverse problems, in "Monte Carlo and Quasi Monte Carlo Methods 2002," Springer, Berlin, (2004), 227-241.       
10 Carole K. Hayakawa, Jerome Spanier, and Frédéric Bevilacqua, et al., Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues, Optics Letters, 26 (2001), 1333-1337.
11 Jari P. Kaipio and Erkki Somersalo, "Statistical and Computational Inverse Problems," Applied Mathematical Sciences, 160, Springer Verlag, New York, 2005.       
12 Jari P. Kaipio and Erkki Somersalo, Statistical inverse problems: Discretization, model reduction, and inverse crimes, Journal of Computational and Applied Mathematics, 198 (2007), 493-504.       
13 Ian Langmore, Anthony Davis and Guillaume Bal, Multi-pixel retrieval of structural and optical parameters in a 2D scene with a path-recycling Monte Carlo forward model and a new Bayesian inference engine, IEEE TGRS, (2012).
14 Jun S. Liu, "Monte Carlo Strategies in Scientific Computing," Springer Series in Statistics, Springer, New York, 2008.       
15 David Moulton, Colin Fox and Daniil Svyatskiy, Multilevel approximations in sample-based inversion from the Dirichlet-to-Neumann map, Journal of Physics: Conference Series, (2008), pp. 124.
16 Hanna K. Pikkarainen, State estimation approach to nonstationary inverse problems: Discretization error and filtering problem, Inverse Problems, 22 (2006), 365-379.       
17 Christian Robert and George Casella, "Monte Carlo Statistical Methods," Second edition, Springer Texts in Statistics, Springer-Verlag, New York, 2004.       
18 Luke Tierney, Markov chains for exploring posterior distributions, The Annals of Statistics, 22 (1994), 1701-1762.       

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