DREAM(D): An adaptive Markov Chain Monte Carlo simulation algorithm to solve discrete, noncontinuous, and combinatorial posterior parameter estimation problems

Hydrology and Earth System Sciences

Volumn 15, Issue 12, 2011, Pages 3701-3713

  Vrugt, J A ^a,b   Ter Braak, C J F ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

^c WAGENINGEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN APPROACHES; BUILDING BLOCKES; COMBINATORIAL OPTIMIZATION PROBLEMS; CONTINUOUS VARIABLES; DETAILED BALANCE; DISCRETE SAMPLING; EFFICIENT SAMPLING; ENVIRONMENTAL MODELING; ERGODICITY; FIXED POINTS; MARKOV CHAIN MONTE CARLO SIMULATION; OPTIMAL EXPERIMENTAL DESIGNS; PARAMETER SPACES; PREDICTIVE UNCERTAINTY; PROPOSAL DISTRIBUTION; RUNOFF MODEL; SOIL WATER RETENTION CURVES;

ADAPTIVE ALGORITHMS; BAYESIAN NETWORKS; BENCHMARKING; BUILDING CODES; COMBINATORIAL OPTIMIZATION; COMPUTER SIMULATION; MARKOV PROCESSES; MONTE CARLO METHODS; OPTIMIZATION; PARAMETER ESTIMATION; SAMPLING; SOIL MOISTURE;

COMBINATORIAL MATHEMATICS;

ALGORITHM; BAYESIAN ANALYSIS; CALIBRATION; ESTIMATION METHOD; MARKOV CHAIN; MONTE CARLO ANALYSIS; NUMERICAL MODEL; OPTIMIZATION; PARAMETERIZATION; RUNOFF; SAMPLING; SOIL WATER; UNCERTAINTY ANALYSIS;

EID: 83755225865     PISSN: 10275606     EISSN: 16077938     Source Type: Journal    
DOI: 10.5194/hess-15-3701-2011     Document Type: Article

References (44)

1. Box, G. E. P. and Tiao, G. C.: Bayesian Inference in Statistical Analyses Addison-Wesley-Longman, Reading, Massachusetts, 1973.
2. Denison, D. G. T., Holmes, C. C., Mallick, B. K., and Smith, A. F. M.: Bayesian methods for nonlinear classification and regression, John Wiley & Sons, Chicester, 2002.
3. Duan, Q., Gupta, V. K., and Sorooshian, S.: Effective and efficient global optimization for conceptual rainfall-runoff models, Water Resour. Res., 28, 1015-1031, 1992.
4. Duan, Q., Schaake, J., Andréassian, V., Franks, S., Goteti, G., Gupta, H. V., Gusev, Y. M., Habets, F., Hall, A., Hay, L., Hogue, T., Huang, M., Leavesley, G., Liang, X., Nasonova, O. N., Noilhan, J., Oudin, L., Sorooshian, S., Wagener, T., and Wood, E.F.: Model Parameter Estimation Experiment (MOPEX): An overview of science strategy and major results from the second and third workshops, J. Hydrol., 320, 3-17, 2006.
5. Furman, A., Ferré, T. P. A., and Warrick, A. W.: Optimization of ERT surveys for monitoring transient hydrological events using perturbation sensitivity and genetic algorithms, Vadose Zone J., 3, 1230-1239, 2004.
6. Gelfand, A. E. and Smith, A. F.: Sampling based approaches to calculating marginal densities, J. Am. Stat. Assoc., 85, 398-409, 1990.
7. Gelman, A. G. and Rubin, D. B.: Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457-472, 1992.
8. Gilks, W. R. and Roberts, G. O.: Strategies for improving MCMC, in: Markov Chain Monte Carlo in Practice, edited by: Gilks, W. R., Richardson, S., and Spiegelhalter, D. J., Chapman & Hall, London, 89-114, 1996.
9. Gilks, W. R., Roberts, G. O., and George, E. I.: Adaptive direction sampling, Statistician, 43, 179-189, 1994.
10. Green, P. J.: Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination, Biometrika, 82, 711-732, 1995.
11. Hastings, W. K.: Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109, 1970.
12. Haario, H., Saksman, E., and Tamminen, J.: Adaptive proposal distribution for random walk Metropolis algorithm, Computation. Stat., 14, 375-395, 1999.
13. Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223-242, 2001. (Pubitemid 33793059)
14. Haario, H., Saksman, E., and Tamminen, J.: Componentwise adaptation for high dimensional MCMC, Computation. Stat., 20, 265-274, 2005.
15. Haario, H., Laine, M., Mira, A., and Saksman, E.: DRAM: Efficient adaptive MCMC, Stat. Comput., 16, 339-354, 2006. (Pubitemid 44581755)
16. Harmancioglu, N. B., Icaga, Y., and Gul, A.: The use of an optimization method in assessment of water quality sampling sites, European Water, 5/6, 25-35, 2004.
17. Hayes, B.: Unwed numbers, American Scientist, 94, 12-15, doi:10.1511/2006.1.12, 2006.
18. Kavetski, D., Kuczera, G., and Franks, S. W.: Bayesian analysis of input uncertainty in hydrologic modeling: 2. Application, Water Resour. Res., 42, W03408, doi:10.1029/2005WR004376, 2006.
19. Kleidorfer, M., Möderl, M., Fach, S., and Rauch, W.: Optimization of measurement campaigns for calibration of a hydrological model, Proceedings of the 11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, 2008.
20. Krink, T., Mittnik, S., and Paterlini, S.: Differential Evolution and Combinatorial Search for Constrained Index Tracking, Center for Studies in Banking and Finance, 09032, Universita di Modena e Reggio Emilia, Facoltdi Economia "Marco Biagi", 2009.
21. Kuczera, G., Kavetski, D., Franks, F. W., and Thyer, M. T.: Towards a Bayesian total error analysis of conceptual rainfallrunoff models: Characterising model error using stormdependent parameters, J. Hydrol., 331, 161-177, 2006. (Pubitemid 44646456)
22. Laloy, E. and Vrugt, J. A.: High-dimensional posterior exploration of hydrologic models using multi-try DREAM(ZS) and high performance computing, Water Resour. Res., in review, doi:2011WR010608RR, 2011.
23. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M. N., Teller, A. H., and Teller, E.: Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087-1092, 1953.
24. Neuman, S. P., Xue, L., Ye, M., and Lu, D.: Bayesian analysis of data-worth considering model and parameter uncertainties, Adv. Water Resour., doi:10.1016/j.advwatres.2011.02.007, in press, 2011.
25. Perrin, C., Andréassian, V., Rojas Serna, C., Mathevet, T., and Le Moine, N.: Discrete parameterization of hydrological models: Evaluating the use of parameter sets libraries over 900 catchments, Water Resour. Res., 44, W08447, doi:10.1029/2007WR006579, 2008.
26. Price, K. V., Storn, R. M., and Lampinen, J. A.: Differential Evolution, A Practical Approach to Global Optimization, Springer, Berlin, 2005.
27. Roberts, G. O. and Gilks,W. R.: Convergence of adaptive direction sampling, J. Multivariate Anal., 49, 287-298, 1994.
28. Roberts, G. O. and Rosenthal, J. S.: Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms, J. Appl. Probab., 44, 458-475, 2007.
29. Roberts, G. O. and Rosenthal, J. S.: Examples of adaptive MCMC, online manucript, available at: Http://probability.ca/jeff/ftpdir/adaptex.pdf, 2008.
30. Roberts, G. O. and Rosenthal, J. S.: Optimal scaling for various Metropolis-Hastings algorithms, Statist. Sci., 16, 351-367, 2001. (Pubitemid 33636356)
31. Schaefli, B., Talamba, D. B., and Musy, A.: Quantifying hydrological modeling errors through a mixture of normal distributions, J. Hydrol., 332, 303-315, 2007. (Pubitemid 44969651)
32. Schoups, G. and Vrugt, J. A.: A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic and non-gaussian errors, Water Resour. Res., 46, W10531, doi:10.1029/ 2009WR008933, 2010.
33. Smith, T. J. and Marshall, L. A.: Bayesian methods in hydrologic modeling: A study of recent advancements in Markov chain Monte Carlo techniques,Water Resour. Res., 44, W00B05, doi:10.1029/2007WR006705, 2008.
34. Sorooshian, S. and Dracup, J. A.: Stochastic parameter estimation procedures for hydrologic rainfall-runoff models: Correlated and heteroscedastic error cases, Water Resour. Res., 16, 430-442, doi:10.1029/WR016i002p00430, 1980.
35. Storn, R. and Price, K.: Differential evolution a simple and efficient heuristic for global optimization over continuous spaces, Global Optimization, 11, pp. 341-359, 1997. (Pubitemid 127502202)
36. Ter Braak, C. J. F.: A Markov chain Monte Carlo version of the genetic algorithm differential evolution: Easy Bayesian computing for real parameter spaces, Stat. Comput., 16, 239-249, 2006. (Pubitemid 43992692)
37. Ter Braak, C. J. F. and Vrugt, J. A.: Differential evolution Markov chain with snooker updater and fewer chains, Stat. Comput., 16, 239-249, doi:10.1007/s11222-008-9104-9, 2008.
38. van Genuchten, M. Th.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898, 1980.
39. Vrugt, J. A., Bouten,W., Gupta, H. V., and Sorooshian, S.: Toward improved identifiability of hydrologic model parameters: The information content of experimental data, Water Resour. Res., 38, 1312, doi:10.1029/2001WR001118, 2002.
40. Vrugt, J. A., Gupta, H. V., Bouten, W., and Sorooshian, S.: A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters, Water Resour. Res., 39, 1-14, doi:10.1029/2002WR001642, 2003.
41. Vrugt, J. A., ter Braak, C. J. F., Clark, M. P., Hyman, J. M., and Robinson, B. A.: Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation,Water Resour. Res., 44, W00B09, doi:10.1029/2007WR006720, 2008.
42. Vrugt, J. A., ter Braak, C. J. F., Diks, C. G. H., Higdon, D., Robinson, B. A., and Hyman, J. M.: Accelerating Markov chain Monte Carlo simulation by differential evolution with selfadaptive randomized subspace sampling, I. J. Nonlin. Sci. Num., 10, 271-288, 2009a.
43. Vrugt, J. A., ter Braak, C. J. F., Gupta, H. V., and Robinson, B. A.: Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?, Stoch. Env. Res. Risk A., 23, 1011-1026, doi:10.1007/s00477-008-0274-y, 2009b.
44. Vrugt, J. A., Laloy, E., and ter Braak, C. J. F.: Differential evolution adaptive Metropolis with sampling from past states, SIAM J. Optimiz., in preparation, 2011.