Bayesian Model Averaging With Fixed and Flexible Priors: Theory, Concepts, and Calibration Experiments for Rainfall-Runoff Modeling

This paper introduces for the first time the concept of Bayesian model averaging (BMA) with multiple prior structures, for rainfall-runoff modeling applications. The original BMA model proposed by Raftery et al. (2005, ) assumes that the prior probability density function (pdf) is adequately described by a mixture of Gamma and Gaussian distributions. Here we discuss the advantages of using BMA with fixed and flexible prior distributions. Uniform, Binomial, Binomial-Beta, Benchmark, and Global Empirical Bayes priors along with Informative Prior Inclusion and Combined Prior Probabilities were applied to calibrate daily streamflow records of a coastal plain watershed in the southeast United States. Various specifications for Zellner'sgprior including Hyper, Fixed, and Empirical Bayes Local (EBL)gpriors were also employed to account for the sensitivity of BMA and derive the conditional pdf of each constituent ensemble member. These priors were examined using the simulation results of conceptual and semidistributed rainfall-runoff models. The hydrologic simulations were first coupled with a new sensitivity analysis model and a parameter uncertainty algorithm to assess the sensitivity and uncertainty associated with each model. BMA was then used to subsequently combine the simulations of the posterior pdf of each constituent hydrological model. Analysis suggests that a BMA based on combined fixed and flexible priors provides a coherent mechanism and promising results for calculating a weighted posterior probability compared to individual model calibration. Furthermore, the probability of Uniform and Informative Prior Inclusion priors received significantly lower predictive error, whereas more uncertainty resulted from a fixedgprior (i.e., EBL).