Non-Informative Priors in Hydrology

Bayesian methods play a prominent role in parameter estimation and uncertainty quantification. In a typical application of Bayes theorem, a prior distribution over the parameters is updated through a likelihood function to obtain the posterior distribution. In the absence of any prior knowledge, a non-informative prior is chosen to express lack of any preference by assigning a uniform distribution over the possible ranges of parameters. However, the validity of uniform priors as being truly non-informative is seldom questioned. The objective of this study is to test this assumption while estimating soil saturated hydraulic conductivity using data from infiltration experiments. The concept of a non-informative prior using an information theoretic approach is pursued for this application, and the results compared to those obtained from assignment of a uniform prior. Non-informative priors obtained by the information theoretic approach are different from a uniform prior, and estimates of the posterior distribution are influenced by the choice of the prior, especially when data are limited. Examples from both hypothetical and real data are utilized to highlight the importance of selecting truly non-informative priors.