Articles | Volume 15, issue 12
Hydrol. Earth Syst. Sci., 15, 3701–3713, 2011
Hydrol. Earth Syst. Sci., 15, 3701–3713, 2011

Research article 13 Dec 2011

Research article | 13 Dec 2011

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

J. A. Vrugt1,2 and C. J. F. Ter Braak3 J. A. Vrugt and C. J. F. Ter Braak
  • 1Department of Civil and Environmental Engineering, University of California, Irvine, 4130 Engineering Gateway, Irvine, CA 92697-2175, USA
  • 2Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, The Netherlands
  • 3Biometris, Wageningen University and Research Centre, P.O. Box 100, 6700 AC, Wageningen, The Netherlands

Abstract. Formal and informal Bayesian approaches have found widespread implementation and use in environmental modeling to summarize parameter and predictive uncertainty. Successful implementation of these methods relies heavily on the availability of efficient sampling methods that approximate, as closely and consistently as possible the (evolving) posterior target distribution. Much of this work has focused on continuous variables that can take on any value within their prior defined ranges. Here, we introduce theory and concepts of a discrete sampling method that resolves the parameter space at fixed points. This new code, entitled DREAM(D) uses the recently developed DREAM algorithm (Vrugt et al., 2008, 2009a, b) as its main building block but implements two novel proposal distributions to help solve discrete and combinatorial optimization problems. This novel MCMC sampler maintains detailed balance and ergodicity, and is especially designed to resolve the emerging class of optimal experimental design problems. Three different case studies involving a Sudoku puzzle, soil water retention curve, and rainfall – runoff model calibration problem are used to benchmark the performance of DREAM(D). The theory and concepts developed herein can be easily integrated into other (adaptive) MCMC algorithms.