Uncertainty Quantification of Complex System Models: Bayesian Analysis

[1]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[2]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[3]  T. Page,et al.  Predictive Capability in Estimating Changes in Water Quality: Long-Term Responses to Atmospheric Deposition , 2004 .

[4]  A. P. Annan,et al.  Electromagnetic determination of soil water content: Measurements in coaxial transmission lines , 1980 .

[5]  Jim Freer,et al.  Uncertainties in data and models to describe event dynamics of agricultural sediment and phosphorus transfer. , 2009, Journal of environmental quality.

[6]  B. Bates,et al.  A Markov Chain Monte Carlo Scheme for parameter estimation and inference in conceptual rainfall‐runoff modeling , 2001 .

[7]  Heikki Haario,et al.  Adaptive proposal distribution for random walk Metropolis algorithm , 1999, Comput. Stat..

[8]  Bruce A. Robinson,et al.  Treatment of uncertainty using ensemble methods: Comparison of sequential data assimilation and Bayesian model averaging , 2007 .

[9]  Keith Beven,et al.  Uncertainty assessment of a process-based integrated catchment model of phosphorus , 2009 .

[10]  J. Nash.  A unit hydrograph study, with particular reference to British catchments [Discussion] , 1960 .

[11]  Jasper A. Vrugt,et al.  Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation , 2016, Environ. Model. Softw..

[12]  Peter Reichert,et al.  Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland) , 2007 .

[13]  Yuqiong Liu,et al.  Reconciling theory with observations: elements of a diagnostic approach to model evaluation , 2008 .

[14]  H. Vereecken,et al.  Inverse modelling of in situ soil water dynamics: accounting for heteroscedastic, autocorrelated, and non-Gaussian distributed residuals , 2015 .

[15]  George Kuczera,et al.  Pitfalls and improvements in the joint inference of heteroscedasticity and autocorrelation in hydrological model calibration , 2013 .

[16]  Keith Beven,et al.  Modelling the chloride signal at Plynlimon, Wales, using a modified dynamic TOPMODEL incorporating conservative chemical mixing (with uncertainty) , 2007 .

[17]  S. Sorooshian,et al.  A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters , 2002 .

[18]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[19]  Cajo J. F. ter Braak,et al.  Differential Evolution Markov Chain with snooker updater and fewer chains , 2008, Stat. Comput..

[20]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[21]  Jasper A. Vrugt,et al.  High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM(ZS) and high‐performance computing , 2012 .

[22]  Florian Pappenberger,et al.  Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions , 2010 .

[23]  Keith Beven,et al.  Modelling the Chloride Signal at the Plynlimon Catchments, Wales Using a Modified Dynamic TOPMODEL. , 2007 .

[24]  Heikki Haario,et al.  Componentwise adaptation for high dimensional MCMC , 2005, Comput. Stat..

[25]  J. Vrugt,et al.  Approximate Bayesian Computation using Markov Chain Monte Carlo simulation: DREAM(ABC) , 2014 .

[26]  Jasper A. Vrugt,et al.  UvA-DARE ( Digital Academic Repository ) DREAM ( D ) : An adaptive Markov chain Monte Carlo simulation algorithm to solve discrete , noncontinuous , and combinatorial posterior parameter estimation problems , 2011 .

[27]  J. Bernardo,et al.  THE FORMAL DEFINITION OF REFERENCE PRIORS , 2009, 0904.0156.

[28]  George Kuczera,et al.  Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation , 2011 .

[29]  Peter Reichert,et al.  Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time‐dependent parameters , 2009 .

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

[31]  S. P. Neuman,et al.  On model selection criteria in multimodel analysis , 2007 .

[32]  Sanjay Shukla,et al.  Eddy covariance‐based evapotranspiration for a subtropical wetland , 2014 .

[33]  J. Vrugt,et al.  Toward diagnostic model calibration and evaluation: Approximate Bayesian computation , 2013 .

[34]  Keith Beven,et al.  Fuzzy set approach to calibrating distributed flood inundation models using remote sensing observations , 2006 .

[35]  Willem Bouten,et al.  A Computer-Controlled 36-Channel Time Domain Reflectometry System for Monitoring Soil Water Contents , 1990 .

[36]  Karel J. Keesman,et al.  Membership-set estimation using random scanning and principal componet analysis , 1990 .

[37]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[38]  Tom Kompas,et al.  Determinants of residential water consumption: Evidence and analysis from a 10‐country household survey , 2011 .

[39]  Keith Beven,et al.  Investigating the Uncertainty in Predicting Responses to Atmospheric Deposition using the Model of Acidification of Groundwater in Catchments (MAGIC) within a Generalised Likelihood Uncertainty Estimation (GLUE) Framework , 2003 .

[40]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[41]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[42]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[43]  H. Jeffreys.  An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[44]  Keith Beven,et al.  Calibration of hydrological models using flow-duration curves , 2010 .

[45]  Wasserman,et al.  Bayesian Model Selection and Model Averaging. , 2000, Journal of mathematical psychology.

[46]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[47]  M. Steel,et al.  On Bayesian Modelling of Fat Tails and Skewness , 1998 .

[48]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[49]  D. Higdon,et al.  Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling , 2009 .

[50]  Dmitri Kavetski,et al.  Pursuing the method of multiple working hypotheses for hydrological modeling , 2011 .

[51]  Sandy L. Zabell,et al.  The rule of succession , 1989 .

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

[53]  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..

[54]  D. Kavetski,et al.  Towards a Bayesian total error analysis of conceptual rainfall-runoff models: Characterising model error using storm-dependent parameters , 2006 .

[55]  J. Rosenthal,et al.  Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms , 2007, Journal of Applied Probability.

[56]  George Kuczera,et al.  Bayesian analysis of input uncertainty in hydrological modeling: 2. Application , 2006 .

[57]  Jasper A. Vrugt,et al.  Embracing equifinality with efficiency : Limits of Acceptability sampling using the DREAM(LOA) algorithm , 2018 .

[58]  George E. P. Box,et al.  Bayesian Inference in Statistical Analysis: Box/Bayesian , 1992 .

[59]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[60]  Jun S. Liu,et al.  The Multiple-Try Method and Local Optimization in Metropolis Sampling , 2000 .

[61]  A. Raftery,et al.  Using Bayesian Model Averaging to Calibrate Forecast Ensembles , 2005 .

[62]  C. Diks,et al.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation , 2005 .

[63]  Walter R. Gilks,et al.  Adaptive Direction Sampling , 1994 .

[64]  M. Schaap,et al.  ROSETTA: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions , 2001 .

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

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

[67]  Andrew Binley,et al.  GLUE: 20 years on , 2014 .

[68]  Chao Yang,et al.  Learn From Thy Neighbor: Parallel-Chain and Regional Adaptive MCMC , 2009 .

[69]  Michael Herbst,et al.  UvA-DARE ( Digital Academic Repository ) Inverse modelling of in situ soil water dynamics : investigating the effect of different prior distributions of the soil hydraulic parameters , 2011 .

[70]  M. Trosset,et al.  Bayesian recursive parameter estimation for hydrologic models , 2001 .

[71]  G. Roberts,et al.  Convergence of adaptive direction sampling , 1994 .

[72]  S. Sorooshian,et al.  Stochastic parameter estimation procedures for hydrologie rainfall‐runoff models: Correlated and heteroscedastic error cases , 1980 .

[73]  Philip John Binning,et al.  Pseudokinetics arising from the upscaling of geochemical equilibrium , 2008 .

[74]  Elena Volpi,et al.  The stationarity paradigm revisited: Hypothesis testing using diagnostics, summary metrics, and DREAM(ABC) , 2015 .

[75]  J. McDonnell,et al.  Constraining dynamic TOPMODEL responses for imprecise water table information using fuzzy rule based performance measures , 2004 .

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

[77]  M. Schaap,et al.  Neural network analysis for hierarchical prediction of soil hydraulic properties , 1998 .

[78]  Reply to comment by Chu et al. on “High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM (ZS) and high‐performance computing” , 2014 .

[79]  Elena Volpi,et al.  Sworn testimony of the model evidence: Gaussian Mixture Importance (GAME) sampling , 2017 .

[80]  Stephen M. Stigler,et al.  Who Discovered Bayes's Theorem? , 1983 .

[81]  Keith Beven,et al.  The future of distributed models: model calibration and uncertainty prediction. , 1992 .

[82]  Jim Freer,et al.  Towards a limits of acceptability approach to the calibration of hydrological models : Extending observation error , 2009 .

[83]  K. Beven,et al.  A limits of acceptability approach to model evaluation and uncertainty estimation in flood frequency estimation by continuous simulation: Skalka catchment, Czech Republic , 2009 .

[84]  George Kuczera,et al.  Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory , 2006 .

[85]  K. Beven,et al.  Uncertainty in the calibration of effective roughness parameters in HEC-RAS using inundation and downstream level observations , 2005 .

[86]  W. Nowak,et al.  Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence , 2014, Water resources research.

[87]  Adrian E. Raftery,et al.  [Practical Markov Chain Monte Carlo]: Comment: One Long Run with Diagnostics: Implementation Strategies for Markov Chain Monte Carlo , 1992 .

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

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

[90]  G. Kuczera.  Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty , 1983 .

[91]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[92]  Heikki Haario,et al.  DRAM: Efficient adaptive MCMC , 2006, Stat. Comput..