Comparing Nonlinear Regression and Markov Chain Monte Carlo Methods for Assessment of Prediction Uncertainty in Vadose Zone Modeling

In vadose zone modeling, parameter estimates and model predictions are inherently uncertain, regardless of quality and quantity of data used in model‐data fusion. Accurate quantification of the uncertainty is necessary to design future data collection for improving the predictive capability of models. This study is focused on evaluating predictive performance of two commonly used methods of uncertainty quantification: nonlinear regression and Bayesian methods. The former quantifies predictive uncertainty using the regression confidence interval (RCI), whereas the latter uses the Bayesian credible interval (BCI); neither RCI nor BCI includes measurement errors. When measurement errors are considered, the counterparts of RCI and BCI are regression prediction interval (RPI) and Bayesian prediction interval (BPI), respectively. The predictive performance is examined through a cross‐validation study of two‐phase flow modeling, and predictive logscore is used as the performance measure. The linear and nonlinear RCI and RPI are evaluated using UCODE_2005. The nonlinear RCI performs better than the linear RCI, and the nonlinear RPI outperforms the linear RPI. The Bayesian intervals are calculated using Markov Chain Monte Carlo (MCMC) techniques implemented with the differential evolution adaptive metropolis (DREAM) algorithm. The BCI/BPI obtained from DREAM has better predictive performance than the linear and nonlinear RCI/RPI. Different from observations in other studies, it is found that estimating nonlinear RCI/RPI is not computationally more efficient than estimating BCI/BPI in this case with low‐dimensional parameter space and a large number of predictions. MCMC methods are thus more appealing than nonlinear regression methods for uncertainty quantification in vadose zone modeling.