The Role of Prior Probabilities on Parameter Estimation in Hydrological Models

Abstract

Bayes theorem provides a formal framework for combining prior and sample information for parameter estimation in the presence of measurement and structural errors. Prior knowledge, however, may not always be available or may be too vague to incorporate into a prior distribution. In such cases, a reference prior must be chosen for an objective analysis. Typically, a uniform density over the possible ranges of parameters is chosen as the reference prior. However, the validity of a uniform prior as a reference prior is seldom questioned. In this study, an information-theoretic approach is pursued to derive reference priors, and the results are compared to those obtained by using a uniform prior. Examples of estimating saturated hydraulic conductivity are presented. Priors over hydraulic conductivity obtained by using the information-theoretic approach are transformation-invariant and typically nonuniform. The choice between information-theoretic and uniform prior influences the posterior distribution of hydraulic conductivity, when sample information is small. The use of reference prior is also demonstrated through the PDG-GIUH hydrologic model, and issues of computational tractability are addressed.