Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

Ahrens, 2014, Reconciling 14C and minirhizotron-based estimates of fine-root turnover with survival functions, J. Plant Nutr. Soil Sci., 177, 287, 10.1002/jpln.201300110 Barthel, 2011, The diel imprint of leaf metabolism on the δ13 13C signal of soil respiration under control and drought conditions, New Phytol., 192, 925, 10.1111/j.1469-8137.2011.03848.x Bates, 2001, A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling, Water Resour. Res., 37, 937, 10.1029/2000WR900363 Bauwens, 2011, 1 Beven, 2006, A manifesto for the equifinality thesis, J. Hydrol., 320, 18, 10.1016/j.jhydrol.2005.07.007 Beven, 1992, “The future of distributed models: model calibration and uncertainty prediction, Hydrol. Process., 6, 279, 10.1002/hyp.3360060305 Beven, 2014, GLUE: 20 years on, Hydrol. Process., 28, 5879 Beven, 2001, “Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, 11, 10.1016/S0022-1694(01)00421-8 Bikowski, 2012, Inversion and sensitivity analysis of ground penetrating radar data with waveguide dispersion using deterministic and Markov chain Monte Carlo methods, Near Surf. Geophys., 10, 641, 10.3997/1873-0604.2012041 Blasone, 2008, Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov chain Monte Carlo sampling, Adv. Water Resour., 31, 630, 10.1016/j.advwatres.2007.12.003 Braakhekke, 2013, Modeling the vertical soil organic matter profile using Bayesian parameter estimation, Biogeosciences, 10, 399, 10.5194/bg-10-399-2013 Brooks, 1998, General methods for monitoring convergence of iterative simulations, J. Comput. Graph. Stat., 7, 434 Chauvenet, 1960, 474 Chib, 1995, Marginal likelihood from the Gibbs output, J. Am. Stat. Assoc., 90, 1313, 10.1080/01621459.1995.10476635 Clark, 2010, Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes, Water Resour. Res., 46, W10510, 10.1029/2009WR008894 Coelho, 2011, A Bayesian framework for parameter estimation in dynamical models, PLoS ONE, 6, e19616, 10.1371/journal.pone.0019616 Davis, 2011, Fast solution of geophysical inversion using adaptive mesh, space-filling curves and wavelet compression, Geophys. J. Int., 185, 157, 10.1111/j.1365-246X.2011.04929.x DeCaluwe, 2014, Phase segregation of sulfonate groups in Nafion interface lamellae, quantified via neutron reflectometry fitting techniques for multi-layered structures, Soft Matter, 10, 5763, 10.1039/C4SM00850B Dekker, 2010, Significant variation in vegetation characteristics and dynamics from ecohydrologic optimality of net carbon profit, Ecohydrology, 5, 1, 10.1002/eco.177 Dempster, 1977, “Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc., 39, 1 Denison, 2002 Duan, 2006, “Model parameter estimation Experiment (MOPEX): an overview of science strategy and major results from the second and third workshops, J. Hydrol., 320, 3, 10.1016/j.jhydrol.2005.07.031 Dumont, 2014, “Parameter identification of the STICS crop model, using an accelerated formal MCMC approach, Environ. Model. Softw., 52, 121, 10.1016/j.envsoft.2013.10.022 Dura, 2011, “Porous Mg formation upon dehydrogenation of MgH2 thin films, J. Appl. Phys., 109, 093501, 10.1063/1.3574664 Evin, 2013, “Pitfalls and improvements in the joint inference of heteroscedasticity and autocorrelation in hydrological model calibration, Water Resour. Res., 49, 4518, 10.1002/wrcr.20284 Freer, 1996, “Bayesian estimation of uncertainty in runoff prediction and the value of data: an application of the GLUE approach, Water Resour. Res., 32, 2161, 10.1029/95WR03723 Gelman, 1998, Simulating normalizing constants: from importance sampling to bridge sampling to path sampling, Stat. Sci., 13, 163, 10.1214/ss/1028905934 Gelman, 1992, “Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457, 10.1214/ss/1177011136 Gelman, 2009, Inference from simulations and monitoring convergence, 163 Gelman, 1996, 599 Gentsch, 2014, Carbon isotope discrimination during branch photosynthesis of Fagus sylvatica: a Bayesian modeling approach, Plant Cell Environ., 37, 1516, 10.1111/pce.12262 Geweke, 1992, Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, 169 Gilks, 1996, Strategies for improving MCMC, 89 Gilks, 1994, “Adaptive direction sampling, Statistician, 43, 179, 10.2307/2348942 Green, 1995, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, 82, 711, 10.1093/biomet/82.4.711 Grubbs, 1950, “Sample criteria for testing outlying observations, Ann. Math. Stat., 21, 27, 10.1214/aoms/1177729885 Gupta, 2008, Reconciling theory with observations: elements of a diagnostic approach to model evaluation, Hydrol. Process., 22, 3802, 10.1002/hyp.6989 Haario, 1999, “Adaptive proposal distribution for random walk Metropolis algorithm, Comput. Stat., 14, 375, 10.1007/s001800050022 Haario, 2001, “An adaptive Metropolis algorithm, Bernoulli, 7, 223, 10.2307/3318737 Haario, 2005, Componentwise adaptation for high dimensional MCMC, Stat. Comput., 20, 265, 10.1007/BF02789703 Haario, 2006, DRAM: efficient adaptive MCMC, Stat.Comput., 16, 339, 10.1007/s11222-006-9438-0 Hansen, 2012, Inverse problems with non-trivial priors: efficient solution through sequential Gibbs sampling, Comput. Geosci., 16, 593, 10.1007/s10596-011-9271-1 Hastings, 1970, “Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97, 10.1093/biomet/57.1.97 Hinnell, 2010, “Improved extraction of hydrologic information from geophysical data through coupled hydrogeophysical inversion, Water Resour. Res., 46, W00D40, 10.1029/2008WR007060 Horowitz, 2012, “Electron spin resonance of nitrogen-vacancy centers in optically trapped nanodiamonds, Proc. Natl. Acad. U. S. A., 109, 13493, 10.1073/pnas.1211311109 Iizumi, 2014, “Dependency of parameter values of a crop model on the spatial scale of simulation, J. Adv. Model. Earth Syst., 06 Jafarpour, 2011, “Wavelet reconstruction of geologic facies from nonlinear dynamic flow measurements, IEEE Trans. Geosci. Remote Sens., 49, 1520, 10.1109/TGRS.2010.2089464 Jafarpour, 2009, “Transform-domain sparsity regularization for inverse problems in geosciences, Geophysics, 74, R69, 10.1190/1.3157250 Jafarpour, 2010, “Compressed history matching: exploiting transform-domain sparsity for regularization of nonlinear dynamic data integration problems, Math. Geosci., 42, 1, 10.1007/s11004-009-9247-z Joseph, 2013, Using a parallelized MCMC algorithm in R to identify appropriate likelihood functions for SWAT, Environ. Model. Softw., 46, 292, 10.1016/j.envsoft.2013.03.012 Kass, 1995, Bayes factors, J. Am. Stat. Assoc., 90, 773, 10.1080/01621459.1995.10476572 Kavetski, 2006, Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory, Water Resour. Res., 42, W03407 Kavetski, 2006, Bayesian analysis of input uncertainty in hydrological modeling: 2. Application, Water Resour. Res., 42, W03408 Keating, 2010, Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality, Water Resour. Res., 46, W10517, 10.1029/2009WR008584 Kikuchi, 2015, “Discrimination-inference for measurement selection, Water Resour. Res., XX Kirby, 2013, “Depth-resolved magnetization reversal in nanoporous perpendicular anisotropy multilayers, J. Appl. Phys., 113, 033909, 10.1063/1.4775819 Kow, 2012, “Enhancement of Markov chain monte Carlo convergence speed in vehicle tracking using genetic operator, 270 Krayer, 2014, “Structural and magnetic etch damage in CoFeB, J. Appl. Phys., 115, 17B751, 10.1063/1.4869276 Kuczera, 1983, “Improved parameter inference in catchment models, 1. Evaluating parameter uncertainty, Water Resour. Res., 19, 1151, 10.1029/WR019i005p01151 Kuczera, 2006, “Towards a Bayesian total error analysis of conceptual rainfall-runoff models: characterising model error using storm-dependent parameters, J. Hydrol., 331, 161, 10.1016/j.jhydrol.2006.05.010 Kuczera, 2010, “A limited memory acceleration strategy for MCMC sampling in hierarchical Bayesian calibration of hydrological models, Water Resour. Res., 46, W07602, 10.1029/2009WR008985 Laloy, 2012, “High-dimensional posterior exploration of hydrologic models using multiple-try DREAM(ZS) and high-performance computing, Water Resour. Res., 48, W01526, 10.1029/2011WR010608 Laloy, 2012, “Mass conservative three-dimensional water tracer distribution from Markov chain Monte Carlo inversion of time-lapse ground-penetrating radar data, Water Resour. Res., 48, W07510, 10.1029/2011WR011238 Laloy, 2013, “Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion, Water Resour. Res., 49, 2664, 10.1002/wrcr.20226 Laloy, 2015, “Probabilistic inference of multi-Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction, Water Resour. Res., 51, 4224, 10.1002/2014WR016395 Laplace, 1774, “Mémoire sur la probabilité des causes par les évènements, Mém. l'Acad. R. Sci. Present. Divers Savan, 6, 621 Leventhal, 2013, “Using an epidemiological model for phylogenetic inference reveals density dependence in HIV transmission, Mol. Biol. Evol., 31, 6, 10.1093/molbev/mst172 Lewis, 1997, “Estimating Bayes factors via posterior simulation with the Laplace-Metropolis estimator, J. Am. Stat. Assoc., 92, 648 Linde, 2013, “Distributed soil moisture from crosshole ground-penetrating radar travel times using stochastic inversion, Vadose Zone J., 12, 10.2136/vzj2012.0101 Lise, 2013, “On the job search and precautionary savings, Rev. Econ. Stud., 80, 1086, 10.1093/restud/rds042 Lise, 2012, 1 Liu, 2000, “The multiple-try method and local optimization in metropolis sampling, J. Am. Stat. Assoc., 95, 121, 10.1080/01621459.2000.10473908 Lochbühler, 2015, Summary statistics from training images as prior information in probabilistic inversion, Geophys. J. Int., 201, 157, 10.1093/gji/ggv008 Lochbühler, 2014, “Probabilistic electrical resistivity tomography for a CO2 sequestration analog, J. Appl. Geophys., 107, 80, 10.1016/j.jappgeo.2014.05.013 Lu, 2014, “A computer program for uncertainty analysis integrating regression and Bayesian methods, Environ. Model. Softw., 60, 45, 10.1016/j.envsoft.2014.06.002 Malama, 2013, “Core-scale solute transport model selection using Monte Carlo analysis, Water Resour. Res., 49, 3133, 10.1002/wrcr.20273 Mari, 2011, “Modeling cholera epidemics: the role of waterways, human mobility and sanitation, J. R. Soc. Interface, 9, 376, 10.1098/rsif.2011.0304 McKay, 1979, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239 Meng, 1996, “Simulating ratios of normalizing constants via a simple identity: a theoretical exploration, Stat. Sin., 6, 831 Metropolis, 1953, “Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087, 10.1063/1.1699114 Minasny, 2011, “Confronting uncertainty in model-based geostatistics using Markov chain Monte Carlo simulation, Geoderma, 163, 150, 10.1016/j.geoderma.2011.03.011 Montanari, 2007, “Calibration of hydrological models in the spectral domain: an opportunity for scarcely gauged basins?, Water Resour. Res., 43, W05434, 10.1029/2006WR005184 Mosegaard, 1995, “Monte Carlo sampling of solutions to inverse problems, J. Geophys. Res., 100, 12431, 10.1029/94JB03097 Nott, 2012, “Generalized likelihood uncertainty estimation (GLUE) and approximate Bayesian computation: what's the connection?, Water Resour. Res., 48, 10.1029/2011WR011128 Oware, 2013, “Physically based regularization of hydrogeophysical inverse problems for improved imaging of process-driven systems, Water Resour. Res., 49, 6238, 10.1002/wrcr.20462 Owejan, 2012, “Solid electrolyte interphase in Li-ion batteries: evolving structures measured in situ by neutron reflectometry, Chem. Mater., 24, 2133, 10.1021/cm3006887 Owen, 2005, “A quasi-Monte Carlo metropolis algorithm, Proc. Natl. Acad. Sci. U. S. A., 102, 8844, 10.1073/pnas.0409596102 Partridge, 2011, “Inverse modeling of cloud-aerosol interactions – part I: detailed response surface analysis, Atmos. Chem. Phys., 11, 4749, 10.5194/acpd-11-4749-2011 Partridge, 2012, “Inverse modeling of cloud-aerosol interactions - Part II: sensitivity tests on liquid phase clouds using Markov chain Monte Carlo simulation approach, Atmos. Chem. Phys., 12, 2823, 10.5194/acp-12-2823-2012 Peirce, 1852, “Criterion for the rejection of doubtful observations, Astron. J. II, 45 Price, 2005 Radu, 2009, “Learn from the thy neighbor: parallel-chain and regional adaptive MCMC, J. Am. Stat. Assoc., 104, 1454, 10.1198/jasa.2009.tm08393 Raftery, 1992, “One long run with diagnostics: Implementation strategies for Markov chain Monte Carlo, Stat. Sci., 7, 493, 10.1214/ss/1177011143 Raftery, 2005, “Using Bayesian model averaging to calibrate forecast ensembles, Mon. Weather Rev., 133, 1155, 10.1175/MWR2906.1 Renard, 2010, “Understanding predictive uncertainty in hydrologic modeling: the challenge of identifying input and structural errors, Water Resour. Res., 46, W05521, 10.1029/2009WR008328 Renard, 2011, “Toward a reliable decomposition of predictive uncertainty in hydrological modeling: characterizing rainfall errors using conditional simulation, Water Resour. Res., 47, W11516, 10.1029/2011WR010643 Rinaldo, 2012, “Reassessment of the 2010–2011 Haiti cholera outbreak and rainfall-driven multiseason projections, Proc. Natl. Acad. U. S. A., 109, 6602, 10.1073/pnas.1203333109 Rings, 2012, “Bayesian model averaging using particle filtering and Gaussian mixture modeling: theory, concepts, and simulation experiments, Water Resour. Res., 48, W05520, 10.1029/2011WR011607 Roberts, 2004 Roberts, 1994, “Convergence of adaptive direction sampling, J. Multivar. Anal., 49, 287, 10.1006/jmva.1994.1028 Roberts, 2007, “Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms, J. Appl. Probab., 44, 458, 10.1017/S0021900200117954 Roberts, 1997, “Weak convergence and optimal scaling of random walk Metropolis algorithms, Ann. Appl. Probab., 7, 110, 10.1214/aoap/1034625254 Rosas-Carbajal, 2014, “Two-dimensional probabilistic inversion of plane-wave electromagnetic data: methodology, model constraints and joint inversion with electrical resistivity data, Geophys. J. Int., 196, 1508, 10.1093/gji/ggt482 Ruggeri, 2015, “Systematic evaluation of sequential geostatistical resampling within MCMC for posterior sampling of near-surface geophysical inverse problems, Geophys. J. Int., 202, 961, 10.1093/gji/ggv196 Sadegh, 2013, “Approximate Bayesian Computation in hydrologic modeling: equifinality of formal and informal approaches, Hydrol. Earth Syst. Sci. - Discuss., 10, 4739, 10.5194/hessd-10-4739-2013 Sadegh, 2014, “Approximate Bayesian computation using Markov chain monte Carlo simulation: DREAM(ABC), Water Resour. Res., 50, 10.1002/2014WR015386 Sadegh, 2015, “The soil water characteristic as new class of closed-form parametric expressions for the flow duration curve, Water Resour. Res., XX Sadegh, 2015, “The stationarity paradigm revisited: hypothesis testing using diagnostics, summary metrics, and DREAM(ABC), Water Resour. Res., XX Schaap, 1998, “Neural network analysis for hierarchical prediction of soil water retention and saturated hydraulic conductivity, Soil Sci. Soc. Am. J., 62, 847, 10.2136/sssaj1998.03615995006200040001x Schaap, 2001, “Rosetta: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions, J. Hydrol., 251, 163, 10.1016/S0022-1694(01)00466-8 Scharnagl, 2010, “Information content of incubation experiments for inverse estimation of pools in the Rothamsted carbon model: a Bayesian perspective, Biogeosciences, 7, 763, 10.5194/bg-7-763-2010 Scharnagl, 2011, “Bayesian inverse modeling of soil water dynamics at the field scale: using prior information about the soil hydraulic properties, Hydrol. Earth Syst. Sci., 15, 3043, 10.5194/hess-15-3043-2011 Scharnagl, 2015, “Inverse modelling of in situ soil water dynamics: accounting for heteroscedastic, autocorrelated, and non-Gaussian distributed residuals, Hydrol. Earth Syst. Sci. Discuss., 12, 2155, 10.5194/hessd-12-2155-2015 Schoups, 2010, “A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic and non-gaussian errors, Water Resour. Res., 46, W10531, 10.1029/2009WR008933 Schoups, 2010, “Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models, Water Resour. Res., 46, W10530, 10.1029/2009WR008648 Shafii, 2014, Uncertainty-based multi-criteria calibration of rainfall-runoff models: a comparative study, Stoch. Environ. Res. Risk Assess., 28, 1493, 10.1007/s00477-014-0855-x Šimůnek, 1998, The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated Media, 186 Smith, 2010, “Development of a formal likelihood function for improved Bayesian inference of ephemeral catchments, Water Resour. Res., 46, W12551, 10.1029/2010WR009514 Sorooshian, 1980, Stochastic parameter estimation procedures for hydrologic rainfall-runoff models: correlated and heteroscedastic error cases, Water Resour. Res., 16, 430, 10.1029/WR016i002p00430 Starrfelt, 2014, Bayesian uncertainty assessment of a semi-distributed integrated catchment model of phosphorus transport, Environ. Sci. Process. Impacts, 16, 1578, 10.1039/C3EM00619K Storn, 1997, Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces, J. Glob. Optim., 11, 341, 10.1023/A:1008202821328 Sun, 2013, Dealing with spatial outliers and mapping uncertainty for evaluating the effects of urbanization on soil: a case study of soil pH and particle fractions in Hong Kong, Geoderma, 195–196, 220, 10.1016/j.geoderma.2012.11.017 Tarasevich, 2013, Neutron reflectometry studies of the adsorbed structure of the amelogenin, LRAP, J. Phys. Chem. B, 117, 3098, 10.1021/jp311936j ter Braak, 2006, A Markov chain Monte Carlo version of the genetic algorithm differential evolution: easy Bayesian computing for real parameter spaces, Stat. Comput., 16, 239, 10.1007/s11222-006-8769-1 ter Braak, 2008, Differential evolution Markov chain with snooker updater and fewer chains, Stat. Comput., 18, 435, 10.1007/s11222-008-9104-9 Thiemann, 2001, Bayesian recursive parameter estimation for hydrologic models, Water Resour. Res., 37, 2521, 10.1029/2000WR900405 Toyli, 2012, Measurement and control of single nitrogen-vacancy center spins above 600 K, Phys. Rev. X, 2, 031001 Turner, 2012, Approximate Bayesian computation with differential evolution, J. Math. Psychol., 56, 375, 10.1016/j.jmp.2012.06.004 Upton, 1996, 55 van Genuchten, 1980, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892, 10.2136/sssaj1980.03615995004400050002x Volpi, 2015, Bayesian model selection with DREAM: multi-dimensional integration of the evidence, Water Resour. Res., XX Vrugt, 2015, To be coherently incoherent: GLUE done with DREAM but much more accurate and efficient, J. Hydrol., XX Vrugt, 2015, The scientific method, Bayes theorem, diagnostic model evaluation, and summary metrics as prior information, Hydrol. Process. Vrugt, 2007, Treatment of uncertainty using ensemble methods: comparison of sequential data assimilation and Bayesian model averaging, Water Resour. Res., 43, W01411, 10.1029/2005WR004838 Vrugt, 2013, Toward diagnostic model calibration and evaluation: approximate Bayesian computation, Water Resour. Res., 49, 10.1002/wrcr.20354 Vrugt, 2003, A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters, Water Resour. Res., 39, 1201, 10.1029/2002WR001642 Vrugt, 2005, Improved treatment of uncertainty in hydrologic modeling: combining the strengths of global optimization and data assimilation, Water Resour. Res., 41, W01017, 10.1029/2004WR003059 Vrugt, 2008, Treatment of input uncertainty in hydrologic modeling: doing hydrology backward with Markov chain Monte Carlo simulation, Water Resour. Res., 44, W00B09, 10.1029/2007WR006720 Vrugt, 2008, Ensemble Bayesian model averaging using Markov chain Monte Carlo sampling, Environ. Fluid Mech., 8, 579, 10.1007/s10652-008-9106-3 Vrugt, 2009, Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling, Int. J. Nonlinear Sci. Numer. Simul., 10, 273, 10.1515/IJNSNS.2009.10.3.273 Vrugt, 2009, Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling, Stoch. Environ. Res. Risk Assess., 23, 1011, 10.1007/s00477-008-0274-y Vrugt, 2013, Advancing hydrologic data assimilation using particle Markov chain Monte Carlo simulation: theory, concepts and applications, Adv. Water Resour., 51, 457, 10.1016/j.advwatres.2012.04.002 Whittle, 1953, Estimation and information in stationary time series, Ark. Mat., 2, 423, 10.1007/BF02590998 Wikle, 2010, A general science-based framework for dynamic spatio-temporal models, Test, 19, 417, 10.1007/s11749-010-0209-z Wöhling, 2011, “Multi-response multi-layer vadose zone model calibration using Markov chain Monte Carlo simulation and field water retention data, Water Resour. Res., 47, W04510, 10.1029/2010WR009265 Yale, 2013, “All-optical control of a solid-state spin using coherent dark states, Proc. Natl. Acad. Sci. U. S. A., 110, 7595, 10.1073/pnas.1305920110 Zaoli Zilliox, 2014, “Tree species diversity and abundance as indicators of understory diversity in French mountain forests: Variations of the relationship in geographical and ecological space, For. Ecol. Manag., 321, 105, 10.1016/j.foreco.2013.07.049