Improving Uncertainty Quantification Through Better Bayesian Inference

Abstract:

Estimating the uncertainty associated with hydrologic model predictions across an array of catchments and hydrologic flow regimes is one of the major challenges facing hydrologic modelers. Despite their widespread use for parameter calibration and uncertainty analysis, formal Bayesian approaches require strong assumptions about the nature of model residuals via the likelihood function that may not be well satisfied. Here, we introduce a framework for specifying residual error models (likelihood functions), which seeks to improve the application of Bayesian methods. Residual error models are selected through a nested approach that is both flexible and extendible and integrates many previously employed residual error models. Residual error models were explored using a top-down approach that focused on assessing each on its ability to properly characterize the underlying assumptions. Results from synthetic and real data applications indicated that the adequacy of an individual likelihood function must be considered using a multifaceted assessment strategy. The form of the residual error model was found to significantly impact the calibrated parameter posterior distributions (statistical distributions of the calibrated parameter values), which in turn have the potential to greatly affect the uncertainty estimates.