On uncertainty quantification in hydrogeology and hydrogeophysics

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  Moshe Y. Vardi,et al.  Verification , 1917, Handbook of Automata Theory.

[3]  D. Krige.  A statistical approach to some basic mine valuation problems on the Witwatersrand, by D.G. Krige, published in the Journal, December 1951 : introduction by the author , 1951 .

[4]  G. Matheron.  Principles of geostatistics , 1963 .

[5]  S. Cambanis,et al.  Gaussian Processes and Gaussian Measures , 1972 .

[6]  A. Journel.  Geostatistics for Conditional Simulation of Ore Bodies , 1974 .

[7]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[8]  A. O'Hagan,et al.  Curve Fitting and Optimal Design for Prediction , 1978 .

[9]  A. Tarantola,et al.  Inverse problems = Quest for information , 1982 .

[10]  W. Menke.  Geophysical data analysis : discrete inverse theory , 1984 .

[11]  H. Omre.  Bayesian kriging—Merging observations and qualified guesses in kriging , 1987 .

[12]  W. B. Whalley,et al.  The use of fractals and pseudofractals in the analysis of two-dimensional outlines: Review and further exploration , 1989 .

[13]  Henning Omre,et al.  The Bayesian bridge between simple and universal kriging , 1989 .

[14]  Yoram Rubin,et al.  Simulation of non‐Gaussian space random functions for modeling transport in groundwater , 1991 .

[15]  Yoram Rubin,et al.  Mapping permeability in heterogeneous aquifers using hydrologic and seismic data , 1992 .

[16]  John D. Bredehoeft,et al.  Ground-water models cannot be validated , 1992 .

[17]  M. Stein,et al.  A Bayesian analysis of kriging , 1993 .

[18]  Y. Rubin,et al.  Geophysical‐hydrological identification of field permeabilities through Bayesian updating , 1993 .

[19]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[20]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[21]  R. M. Srivastava,et al.  Multivariate Geostatistics: Beyond Bivariate Moments , 1993 .

[22]  J. Harris,et al.  Coupled seismic and tracer test inversion for aquifer property characterization , 1993 .

[23]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[24]  R. Parker.  Geophysical Inverse Theory , 1994 .

[25]  N Oreskes,et al.  Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences , 1994, Science.

[26]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[27]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[28]  P. Kitanidis.  Quasi‐Linear Geostatistical Theory for Inversing , 1995 .

[29]  D. McLaughlin,et al.  A Reassessment of the Groundwater Inverse Problem , 1996 .

[30]  T. Mukerji,et al.  The Rock Physics Handbook , 1998 .

[31]  M. Bosch.  Lithologic tomography: From plural geophysical data to lithology estimation , 1999 .

[32]  L. Wolpert.  Popper , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[33]  Y. Rubin,et al.  Estimating the hydraulic conductivity at the south oyster site from geophysical tomographic data using Bayesian Techniques based on the normal linear regression model , 2001 .

[34]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[35]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[36]  Stefan Heinrich,et al.  Multilevel Monte Carlo Methods , 2001, LSSC.

[37]  Christian Lantuéjoul,et al.  Geostatistical Simulation: Models and Algorithms , 2001 .

[38]  Keith Beven,et al.  Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology , 2001 .

[39]  D. Balding,et al.  Approximate Bayesian computation in population genetics. , 2002, Genetics.

[40]  Sebastien Strebelle,et al.  Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics , 2002 .

[41]  Panos G. Georgopoulos,et al.  Uncertainty reduction and characterization for complex environmental fate and transport models: An empirical Bayesian framework incorporating the stochastic response surface method , 2003 .

[42]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[43]  Paul Marjoram,et al.  Markov chain Monte Carlo without likelihoods , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[44]  Sw. Banerjee,et al.  Hierarchical Modeling and Analysis for Spatial Data , 2003 .

[45]  M. Beaumont.  Estimation of population growth or decline in genetically monitored populations. , 2003, Genetics.

[46]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[47]  Micha Werner,et al.  Reduction of Monte-Carlo simulation runs for uncertainty estimation in hydrological modelling , 2003 .

[48]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[49]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[50]  Dave Higdon,et al.  Combining Field Data and Computer Simulations for Calibration and Prediction , 2005, SIAM J. Sci. Comput..

[51]  S. Geiger,et al.  Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media , 2004 .

[52]  S. Finsterle,et al.  Estimating flow parameter distributions using ground-penetrating radar and hydrological measurements , 2004 .

[53]  Michael W Deem,et al.  Parallel tempering: theory, applications, and new perspectives. , 2005, Physical chemistry chemical physics : PCCP.

[54]  Andrew Binley,et al.  Applying petrophysical models to radar travel time and electrical resistivity tomograms: Resolution‐dependent limitations , 2005 .

[55]  Andres Alcolea,et al.  Inverse problem in hydrogeology , 2005 .

[56]  T. Hansen,et al.  Identifying Unsaturated Hydraulic Parameters Using an Integrated Data Fusion Approach on Cross‐Borehole Geophysical Data , 2006 .

[57]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[58]  A. Tarantola,et al.  Linear inverse Gaussian theory and geostatistics , 2006 .

[59]  A. O’Sullivan,et al.  Error models for reducing history match bias , 2006 .

[60]  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..

[61]  Yalchin Efendiev,et al.  Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models , 2006, SIAM J. Sci. Comput..

[62]  E. Somersalo,et al.  Approximation errors and model reduction with an application in optical diffusion tomography , 2006 .

[63]  A. Tarantola.  Popper, Bayes and the inverse problem , 2006 .

[64]  Steen Christensen,et al.  Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media , 2006 .

[65]  Christine A. Shoemaker,et al.  A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions , 2007, INFORMS J. Comput..

[66]  Habib N. Najm,et al.  Stochastic spectral methods for efficient Bayesian solution of inverse problems , 2005, J. Comput. Phys..

[67]  J. Caers,et al.  Conditional Simulation with Patterns , 2007 .

[68]  P. Diggle,et al.  Model‐based geostatistics , 2007 .

[69]  James O. Berger,et al.  A Framework for Validation of Computer Models , 2007, Technometrics.

[70]  Jef Caers,et al.  Representing Spatial Uncertainty Using Distances and Kernels , 2009 .

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

[72]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[73]  Bertrand Iooss,et al.  An efficient methodology for modeling complex computer codes with Gaussian processes , 2008, Comput. Stat. Data Anal..

[74]  Michael B. Giles,et al.  Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..

[75]  L. Y. Hu,et al.  Multiple‐point geostatistics for modeling subsurface heterogeneity: A comprehensive review , 2008 .

[76]  P. Bickel,et al.  Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems , 2008, 0805.3034.

[77]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .

[78]  Binayak P. Mohanty,et al.  Efficient uncertainty quantification techniques in inverse problems for Richards’ equation using coarse-scale simulation models , 2009 .

[79]  Y. Marzouk,et al.  A stochastic collocation approach to Bayesian inference in inverse problems , 2009 .

[80]  Johan Alexander Huisman,et al.  Critical Steps for the Continuing Advancement of Hydrogeophysics , 2009 .

[81]  Nicholas Zabaras,et al.  An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method , 2009 .

[82]  Martin Hairer,et al.  An Introduction to Stochastic PDEs , 2009, 0907.4178.

[83]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[84]  H. Vereecken,et al.  Coupled hydrogeophysical parameter estimation using a sequential Bayesian approach , 2009 .

[85]  Knud Skou Cordua,et al.  Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data. , 2009 .

[86]  C. Andrieu,et al.  The pseudo-marginal approach for efficient Monte Carlo computations , 2009, 0903.5480.

[87]  Roussos Dimitrakopoulos,et al.  High-order Statistics of Spatial Random Fields: Exploring Spatial Cumulants for Modeling Complex Non-Gaussian and Non-linear Phenomena , 2009 .

[88]  Stanley H. Cohen,et al.  Design and Analysis , 2010 .

[89]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields; The SPDE approach , 2010 .

[90]  A. Lehikoinen,et al.  Dynamic inversion for hydrological process monitoring with electrical resistance tomography under model uncertainties , 2010 .

[91]  John Doherty,et al.  A short exploration of structural noise , 2010 .

[92]  J. Vrugt,et al.  A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors , 2010 .

[93]  Andrew M. Stuart,et al.  Inverse problems: A Bayesian perspective , 2010, Acta Numerica.

[94]  M. Scheuerer.  Regularity of the sample paths of a general second order random field , 2010 .

[95]  A. Doucet,et al.  Particle Markov chain Monte Carlo methods , 2010 .

[96]  Tyler Smith,et al.  Development of a formal likelihood function for improved Bayesian inference of ephemeral catchments , 2010 .

[97]  Marita Stien,et al.  Facies Modeling Using a Markov Mesh Model Specification , 2011 .

[98]  D. Oliver,et al.  Recent progress on reservoir history matching: a review , 2011 .

[99]  Siddhartha Mishra,et al.  Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions , 2011 .

[100]  M. Canty,et al.  Hydraulic parameter estimation by remotely-sensed top soil moisture observations with the particle filter , 2011 .

[101]  Radford M. Neal.  MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[102]  C. Schwab,et al.  Multi-level Monte Carlo finite volume methods for shallow water equations with uncertain topography in multi-dimensions , 2011 .

[103]  A. Fichtner.  Full Seismic Waveform Modelling and Inversion , 2011 .

[104]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[105]  K. A. Cliffe,et al.  Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients , 2011, Comput. Vis. Sci..

[106]  Andrea Barth,et al.  Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients , 2011, Numerische Mathematik.

[107]  André I. Khuri,et al.  Response surface methodology , 2010 .

[108]  Frances Y. Kuo,et al.  Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients , 2011 .

[109]  Andrew M. Stuart,et al.  Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem , 2011, SIAM J. Numer. Anal..

[110]  Andreas Englert,et al.  Mixing, spreading and reaction in heterogeneous media: a brief review. , 2011, Journal of contaminant hydrology.

[111]  Tiangang Cui,et al.  Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm , 2011 .

[112]  E. Vázquez-Suñé,et al.  Geophysics and hydrogeology: will they ever marry?. , 2012 .

[113]  T. Hansen,et al.  Inverse problems with non-trivial priors: efficient solution through sequential Gibbs sampling , 2012, Computational Geosciences.

[114]  H. Rue,et al.  In order to make spatial statistics computationally feasible, we need to forget about the covariance function , 2012 .

[115]  Andrew M. Stuart,et al.  Complexity analysis of accelerated MCMC methods for Bayesian inversion , 2012, 1207.2411.

[116]  Alberto Guadagnini,et al.  Global sensitivity analysis through polynomial chaos expansion of a basin-scale geochemical compaction model , 2013, Computational Geosciences.

[117]  Ming Ye,et al.  Towards a comprehensive assessment of model structural adequacy , 2012 .

[118]  Bryan A. Tolson,et al.  Review of surrogate modeling in water resources , 2012 .

[119]  K. Holliger,et al.  Bayesian Markov‐Chain‐Monte‐Carlo Inversion of Time‐Lapse Crosshole GPR Data to Characterize the Vadose Zone at the Arrenaes Site, Denmark , 2012 .

[120]  Jonas Sukys,et al.  Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions , 2012, SIAM J. Sci. Comput..

[121]  Helmut Harbrecht,et al.  On Multilevel Quadrature for Elliptic Stochastic Partial Differential Equations , 2012 .

[122]  Wolfgang Nowak,et al.  Parameter Estimation by Ensemble Kalman Filters with Transformed Data , 2010 .

[123]  Jonas Sukys,et al.  Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions , 2012, J. Comput. Phys..

[124]  Frances Y. Kuo,et al.  Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients , 2012, 1208.6349.

[125]  Stan E. Dosso,et al.  Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models , 2012 .

[126]  B. Martin.  PARAMETER ESTIMATION , 2012, Statistical Methods for Biomedical Research.

[127]  Shoou-Yuh Chang,et al.  State and Parameter Estimation with an SIR Particle Filter in a Three-Dimensional Groundwater Pollutant Transport Model , 2012 .

[128]  A. Doucet,et al.  Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator , 2012, 1210.1871.

[129]  D. Pasetto,et al.  Ensemble Kalman filter versus particle filter for a physically-based coupled surface-subsurface model , 2012 .

[130]  D. Mallants,et al.  Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion , 2013 .

[131]  F. Lindgren,et al.  Exploring a New Class of Non-stationary Spatial Gaussian Random Fields with Varying Local Anisotropy , 2013, 1304.6949.

[132]  By Rui Tuo.  A THEORETICAL FRAMEWORK FOR CALIBRATION IN COMPUTER MODELS : PARAMETRIZATION , ESTIMATION AND CONVERGENCE PROPERTIES , 2013 .

[133]  Michael B. Giles,et al.  Multilevel Monte Carlo methods , 2013, Acta Numerica.

[134]  G. Roberts,et al.  MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster , 2012, 1202.0709.

[135]  Robert Scheichl,et al.  Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods , 2013, SIAM J. Numer. Anal..

[136]  Elisabeth Ullmann,et al.  Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients , 2012, Numerische Mathematik.

[137]  Andrea Barth,et al.  Multilevel Monte Carlo method for parabolic stochastic partial differential equations , 2013 .

[138]  Niklas Linde,et al.  3-D characterization of high-permeability zones in a gravel aquifer using 2-D crosshole GPR full-waveform inversion and waveguide detection , 2013 .

[139]  Christian Lantuéjoul,et al.  Can a Training Image Be a Substitute for a Random Field Model? , 2014, Mathematical Geosciences.

[140]  M. Adès,et al.  An exploration of the equivalent weights particle filter , 2013 .

[141]  Philippe Renard,et al.  Distance-based Kriging relying on proxy simulations for inverse conditioning , 2013 .

[142]  Florian Müller,et al.  Multilevel Monte Carlo for two phase flow and Buckley-Leverett transport in random heterogeneous porous media , 2013, J. Comput. Phys..

[143]  Yalchin Efendiev,et al.  Multilevel Monte Carlo methods using ensemble level mixed MsFEM for two-phase flow and transport simulations , 2013, Computational Geosciences.

[144]  W. Illman,et al.  Geostatistical reduced‐order models in underdetermined inverse problems , 2013 .

[145]  Ming Ye,et al.  An adaptive sparse‐grid high‐order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling , 2013 .

[146]  Ivan Lunati,et al.  Local and Global Error Models to Improve Uncertainty Quantification , 2013, Mathematical Geosciences.

[147]  Daniela Calvetti,et al.  Dynamic updating of numerical model discrepancy using sequential sampling , 2014 .

[148]  Sylvain Lefebvre,et al.  Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research , 2014, Comput. Geosci..

[149]  Knud Skou Cordua,et al.  Accounting for imperfect forward modeling in geophysical inverse problems — Exemplified for crosshole tomography , 2014 .

[150]  Liangping Li,et al.  Inverse methods in hydrogeology: Evolution and recent trends , 2014 .

[151]  Florian Müller,et al.  Multilevel Monte Carlo for two phase flow and transport in random heterogeneous porous media , 2012 .

[152]  Christoph Schwab,et al.  N-term Wiener chaos approximation rates for elliptic PDEs with lognormal Gaussian random inputs , 2014 .

[153]  Jef Caers,et al.  Universal kriging with training images , 2015 .

[154]  S. Martino,et al.  Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field , 2014, 1412.2798.

[155]  A. Stuart,et al.  Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions , 2011, 1112.1392.

[156]  Raul Tempone,et al.  A quasi-optimal sparse grids procedure for groundwater flows , 2014 .

[157]  Insa Neuweiler,et al.  Using a bias aware EnKF to account for unresolved structure in an unsaturated zone model , 2014 .

[158]  Jenný Brynjarsdóttir,et al.  Learning about physical parameters: the importance of model discrepancy , 2014 .

[159]  G. Mariéthoz,et al.  Multiple-point Geostatistics: Stochastic Modeling with Training Images , 2014 .

[160]  Arnaud Doucet,et al.  On Particle Methods for Parameter Estimation in State-Space Models , 2014, 1412.8695.

[161]  Hans-Werner van Wyk,et al.  Multilevel Sparse Grid Methods for Elliptic Partial Differential Equations with Random Coeffi cients , 2014, 1404.0963.

[162]  Catherine E. Powell,et al.  An Introduction to Computational Stochastic PDEs , 2014 .

[163]  J. Vrugt,et al.  Summary statistics from training images as prior information in probabilistic inversion , 2015, 1701.01376.

[164]  Max Gunzburger,et al.  A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2014, SIAM/ASA J. Uncertain. Quantification.

[165]  C. F. Wu,et al.  Efficient Calibration for Imperfect Computer Models , 2015, 1507.07280.

[166]  Raul Tempone,et al.  An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient , 2016 .

[167]  Ahmed H. Elsheikh,et al.  Accelerating Monte Carlo Markov chains with proxy and error models , 2015, Comput. Geosci..

[168]  Stephen G. Penny,et al.  A local particle filter for high-dimensional geophysical systems , 2015 .

[169]  Susan S. Hubbard,et al.  The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales , 2015, Water resources research.

[170]  David Ginsbourger,et al.  Functional error modeling for uncertainty quantification in hydrogeology , 2015 .

[171]  Fabio Nobile,et al.  Stochastic Partial Differential Equations: Analysis and Computations a Multi Level Monte Carlo Method with Control Variate for Elliptic Pdes with Log- Normal Coefficients a Multi Level Monte Carlo Method with Control Variate for Elliptic Pdes with Log-normal Coefficients , 2022 .

[172]  P. Renard,et al.  Geological realism in hydrogeological and geophysical inverse modeling: A review , 2015, 1701.01602.

[173]  Matteo Rossi,et al.  An iterative particle filter approach for coupled hydro-geophysical inversion of a controlled infiltration experiment , 2015, J. Comput. Phys..

[174]  H. Najm,et al.  On the Statistical Calibration of Physical Models: STATISTICAL CALIBRATION OF PHYSICAL MODELS , 2015 .

[175]  Michael Andrew Christie,et al.  Surrogate accelerated sampling of reservoir models with complex structures using sparse polynomial chaos expansion , 2015 .

[176]  R. Handel,et al.  Can local particle filters beat the curse of dimensionality , 2013, 1301.6585.

[177]  Albert J. Valocchi,et al.  A Bayesian approach to improved calibration and prediction of groundwater models with structural error , 2015 .

[178]  Frances Y. Kuo,et al.  Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients , 2015, Foundations of Computational Mathematics.

[179]  T. J. Dodwell,et al.  A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow , 2013, SIAM/ASA J. Uncertain. Quantification.

[180]  Jeffrey L. Anderson,et al.  Efficient Assimilation of Simulated Observations in a High-Dimensional Geophysical System Using a Localized Particle Filter , 2016 .

[181]  N. Linde,et al.  Joint Inversion in Hydrogeophysics and Near‐Surface Geophysics , 2016 .

[182]  Simon J. Godsill,et al.  Blocked Particle Gibbs Schemes for High Dimensional Interacting Systems , 2015, IEEE Journal of Selected Topics in Signal Processing.

[183]  Fabio Nobile,et al.  Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity , 2015, Foundations of Computational Mathematics.

[184]  Fabio Nobile,et al.  Multi-index Monte Carlo: when sparsity meets sampling , 2014, Numerische Mathematik.

[185]  J. Poterjoy.  A Localized Particle Filter for High-Dimensional Nonlinear Systems , 2016 .

[186]  Arnaud Doucet,et al.  On embedded hidden Markov models and particle Markov chain Monte Carlo methods , 2016, 1610.08962.

[187]  Raul Tempone,et al.  Multi-Index Stochastic Collocation for random PDEs , 2015, 1508.07467.

[188]  Knud Skou Cordua,et al.  Probabilistic Integration of Geo‐Information , 2016 .

[189]  K. Zygalakis,et al.  Multilevel Monte Carlo for Scalable Bayesian Computations , 2016, 1609.06144.

[190]  M. Bosch.  Inference Networks in Earth Models with Multiple Components and Data , 2016 .

[191]  M. Vihola,et al.  Importance sampling type correction of Markov chain Monte Carlo and exact approximations , 2016 .

[192]  Sumeetpal S. Singh,et al.  Approximate Smoothing and Parameter Estimation in High-Dimensional State-Space Models , 2016, IEEE Transactions on Signal Processing.

[193]  A. M. Stuart,et al.  Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems , 2016, SIAM/ASA J. Uncertain. Quantification.

[194]  A. Stuart,et al.  The Bayesian Approach to Inverse Problems , 2013, 1302.6989.

[195]  Andrew M. Stuart,et al.  Statistical analysis of differential equations: introducing probability measures on numerical solutions , 2016, Statistics and Computing.

[196]  Radford M. Neal,et al.  Sampling Latent States for High-Dimensional Non-Linear State Space Models with the Embedded HMM Method , 2016, Bayesian Analysis.

[197]  ′ Mixing , .

[198]  P. V. Oorschot,et al.  Efficient Implementation , 2022 .