Adaptive Error Modelling in MCMC Sampling for Large Scale Inverse Problems

[1]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[2]  U. Grenander,et al.  Structural Image Restoration through Deformable Templates , 1991 .

[3]  Håvard Rue,et al.  Advances in Bayesian Image Analysis , 2003 .

[4]  D. Freedman,et al.  On the histogram as a density estimator:L2 theory , 1981 .

[5]  Henry P. Wynn,et al.  Screening, predicting, and computer experiments , 1992 .

[6]  Dave Higdon,et al.  A Bayesian approach to characterizing uncertainty in inverse problems using coarse and fine-scale information , 2002, IEEE Trans. Signal Process..

[7]  Martin B. Hansen,et al.  Bayesian inversion of geoelectrical resistivity data , 2003 .

[8]  Robert B. Gramacy,et al.  Ja n 20 08 Bayesian Treed Gaussian Process Models with an Application to Computer Modeling , 2009 .

[9]  M. O'Sullivan.  Geothermal reservoir simulation , 1985 .

[10]  T. J. Mitchell,et al.  Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction , 1993 .

[11]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[12]  J. Rosenthal,et al.  Optimal scaling for various Metropolis-Hastings algorithms , 2001 .

[13]  Tiangang Cui,et al.  Bayesian calibration of geothermal reservoir models via Markov Chain Monte Carlo , 2010 .

[14]  P. Green.  Bayesian reconstructions from emission tomography data using a modified EM algorithm. , 1990, IEEE transactions on medical imaging.

[15]  Øivind Skare,et al.  Coloured Voronoi tessellations for Bayesian image analysis and reservoir modelling , 2001 .

[16]  Eric James Grimme,et al.  Krylov Projection Methods for Model Reduction , 1997 .

[17]  Anne-Mette K. Hein,et al.  BGX: a Bioconductor package for the Bayesian integrated analysis of Affymetrix GeneChips , 2007, BMC Bioinformatics.

[18]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Michael Andrew Christie,et al.  Tenth SPE Comparative Solution Project: a comparison of upscaling techniques , 2001 .

[20]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[21]  H. Haario,et al.  Markov chain Monte Carlo methods for high dimensional inversion in remote sensing , 2004 .

[22]  M. Grant.  Geothermal Reservoir Engineering , 1982 .

[23]  Matti Vihola,et al.  Can the Adaptive Metropolis Algorithm Collapse Without the Covariance Lower Bound , 2009, 0911.0522.

[24]  Anil K. Jain,et al.  Deformable template models: A review , 1998, Signal Process..

[25]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[26]  David Higdon,et al.  A process-convolution approach to modelling temperatures in the North Atlantic Ocean , 1998, Environmental and Ecological Statistics.

[27]  Geoff K. Nicholls,et al.  Statistical inversion of South Atlantic circulation in an abyssal neutral density layer , 2005 .

[28]  M. Opper,et al.  inverse problems: some new approaches , 2022 .

[29]  A. Gelman,et al.  Weak convergence and optimal scaling of random walk Metropolis algorithms , 1997 .

[30]  K. Pruess,et al.  TOUGH2-A General-Purpose Numerical Simulator for Multiphase Fluid and Heat Flow , 1991 .

[31]  Michael I. Miller,et al.  REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .

[32]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[33]  D. Higdon,et al.  Computer Model Calibration Using High-Dimensional Output , 2008 .

[34]  Daniel Watzenig,et al.  A review of statistical modelling and inference for electrical capacitance tomography , 2009 .

[35]  Geoff K. Nicholls,et al.  Prior modeling and posterior sampling in impedance imaging , 1998, Optics & Photonics.

[36]  Jeffrey S. Rosenthal,et al.  Coupling and Ergodicity of Adaptive MCMC , 2007 .

[37]  Karen Willcox,et al.  Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems , 2010, SIAM J. Sci. Comput..

[38]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[39]  Ronald J. Jaszczak,et al.  Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data , 1997, IEEE Transactions on Medical Imaging.

[40]  P. Clifford,et al.  Point-based polygonal models for random graphs , 1993, Advances in Applied Probability.

[41]  J. Rosenthal,et al.  On adaptive Markov chain Monte Carlo algorithms , 2005 .

[42]  Jing-Rebecca Li.  Model reduction of large linear systems via low rank system gramians , 2000 .

[43]  A. Baddeley,et al.  Stochastic geometry models in high-level vision , 1993 .

[44]  E. Saksman,et al.  On the ergodicity of the adaptive Metropolis algorithm on unbounded domains , 2008, 0806.2933.

[45]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[46]  Hans R. Künsch,et al.  Intrinsic autoregressions and related models on the two-dimensional lattice , 1987 .

[47]  E. Somersalo,et al.  Statistical inverse problems: discretization, model reduction and inverse crimes , 2007 .

[48]  J. Besag,et al.  On conditional and intrinsic autoregressions , 1995 .

[49]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[50]  Cajo J. F. ter Braak,et al.  Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation , 2008 .

[51]  Geoff K. Nicholls,et al.  Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models , 1998 .

[52]  J.P. Kaipio,et al.  Three-dimensional electrical impedance tomography based on the complete electrode model , 1999, IEEE Transactions on Biomedical Engineering.

[53]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[54]  I. Weir.  Fully Bayesian Reconstructions from Single-Photon Emission Computed Tomography Data , 1997 .

[55]  Ulli Wolff.  Monte Carlo errors with less errors , 2004 .

[56]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[57]  Cajo J. F. ter Braak,et al.  A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces , 2006, Stat. Comput..