Tools for investigating the prior distribution in Bayesian hydrology

Abstract

Summary Bayesian inference is one of the most popular tools for uncertainty analysis in hydrological modeling. While much emphasis has been placed on the selection of appropriate likelihood functions within Bayesian hydrology, few researchers have evaluated the importance of the prior distribution in deriving appropriate posterior distributions. This paper describes tools for the evaluation of parameter sensitivity to the prior distribution to provide guidelines for defining meaningful priors. The tools described here consist of two measurements, the Kullback-Leibler Divergence (KLD) and the prior information elasticity. The Kullback-Leibler Divergence (KLD) is applied to calculate differences between the prior and posterior distributions for different cases. The prior information elasticity is then used to quantify the responsiveness of the KLD values to the change of prior distributions and length of available data. The tools are demonstrated via a Bayesian framework using an MCMC algorithm for a conceptual hydrologic model with both synthetic and real cases. The results of the application of this toolkit suggest the prior distribution can have a significant impact on the posterior distribution and should be more routinely assessed in hydrologic studies.