INTEGRATION OF MARKOV CHAIN MONTE CARLO SIMULATION INTO UCODE FOR BAYESIAN UNCERTAINTY ANALYSIS

Uncertainty analysis can be quantified using either confidence intervals based on classical regression theories or credible intervals based on Bayesian theories. UCODE_2005 perform uncertainty analysis by calculating regression confidence intervals. In Bayesian uncertainty analysis, the credible intervals are usually evaluated using Markov chain Monte Carlo (MCMC) methods. The differential evolution adaptive Metropolis (DREAM) method, one of the MCMC samplers, can efficiently estimate the posterior probability density function of model parameters in complex, high-dimensional sampling problems. This work implements DREAM algorithm into UCODE_2005. It allows users to conduct Bayesian uncertainty analysis with MCMC simulation within UCODE so that the resulting Bayesian credible intervals can be compared with the regression confidence intervals. The integration makes it possible to directly use UCODE template and instruction files for the Bayesian uncertainty analysis, and this is true for any process models with ASCII-based inputs and outputs. With UCODE derived-equation capability, the Bayesian uncertainty analysis can be conducted for parameters and predictions calculated from values with user-defined equations. In evaluating the Bayesian posterior distribution of parameters, users are allowed to select from eleven generally used probability distributions as the prior distribution. The likelihood function is constructed by assuming Gaussian errors in the observations which leads to the weighted least-squares objective function. The weighting is calculated as the inverse of the covariance matrix of observation errors. The covariance matrix can be diagonal or full, provided by users in flexible ways with UCODE’s a variety of statistics and matrix_files input block. The execution of Bayesian uncertainty analysis in UCODE is conceptually simple and operationally straightforward, similar to executing other capabilities of UCODE. We use a reactive transport model to demonstrate the application of this new feature of UCODE. The integration of DREAM algorithm into UCODE_2005 is intended to provide users with an advanced tool to conduct Bayesian uncertainty analysis in a convenient and flexible way for a variety of environmental problems.