Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation. (January 2016)

• Record Type: Journal Article
• Authors: Vrugt, Jasper A.
• Is Part Of: Environmental modelling & software. Volume 75(2016:Jan.)
• Page Start: 273
• Page End: 316
• Publication Date: 2016-01
• Subjects: Bayesian inference -- Markov chain Monte Carlo (MCMC) simulation -- Random walk metropolis (RWM) -- Adaptive metropolis (AM) -- Differential evolution Markov chain (DE-MC) -- Prior distribution -- Likelihood function -- Posterior distribution -- Approximate Bayesian computation (ABC) -- Diagnostic model evaluation -- Residual analysis -- Environmental modeling -- Bayesian model averaging (BMA) -- Generalized likelihood uncertainty estimation (GLUE) -- Multi-processor computing -- Extended metropolis algorithm (EMA); Environmental monitoring -- Computer programs -- Periodicals; Ecology -- Computer simulation -- Periodicals; Digital computer simulation -- Periodicals; Computer software -- Periodicals; Environmental Monitoring -- Periodicals; Computer Simulation -- Periodicals; Environnement -- Surveillance -- Logiciels -- Périodiques; Écologie -- Simulation, Méthodes de -- Périodiques; Simulation par ordinateur -- Périodiques; Logiciels -- Périodiques; Computer software; Digital computer simulation; Ecology -- Computer simulation; Environmental monitoring -- Computer programs; Periodicals; Electronic journals; 363.70015118
• DOI: 10.1016/j.envsoft.2015.08.013
• Languages: English
• ISSNs: 1364-8152

Abstract

Abstract: Bayesian inference has found widespread application and use in science and engineering to reconcile Earth system models with data, including prediction in space (interpolation), prediction in time (forecasting), assimilation of observations and deterministic/stochastic model output, and inference of the model parameters. Bayes theorem states that the posterior probability, p ( H | Y ˜ ) of a hypothesis, H is proportional to the product of the prior probability, p ( H ) of this hypothesis and the likelihood, L ( H | Y ˜ ) of the same hypothesis given the new observations, Y ˜, or p ( H | Y ˜ ) ∝ p ( H ) L ( H | Y ˜ ) . In science and engineering, H often constitutes some numerical model, ℱ(x) which summarizes, in algebraic and differential equations, state variables and fluxes, all knowledge of the system of interest, and the unknown parameter values, x are subject to inference using the data Y ˜ . Unfortunately, for complex system models the posterior distribution is often high dimensional and analytically intractable, and sampling methods are required to approximate the target. In this paper I review the basic theory of Markov chain Monte Carlo (MCMC) simulation and introduce a MATLAB toolbox of the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm developed by Vrugt et al. (2008a, 2009a) and used for Bayesian inference in fields ranging from physics, chemistry and engineering, to ecology, hydrology, and geophysics. This MATLAB toolbox provides scientists and engineers with an arsenal of options and utilities to solve posterior sampling problems involving (among others) bimodality, high-dimensionality, summary statistics, bounded parameter spaces, dynamic simulation models, formal/informal likelihood functions (GLUE), diagnostic model evaluation, data assimilation, Bayesian model averaging, distributed computation, and informative/noninformative prior distributions. The DREAM toolbox supports parallel computing and includes tools for convergence analysis of the sampled chain trajectories and post-processing of the results. Seven different case studies illustrate the main capabilities and functionalities of the MATLAB toolbox. Highlights: A MATLAB toolbox of the DREAM algorithm is presented. This toolbox provides users with a great arsenal of options for Bayesian inference. The toolbox supports/implements parallel computing. Seven different case studies illustrate the main capabilities and functionalities of the toolbox.