Prior weight dilution in Bayesian model averaging for groundwater modeling

It is unrealistic to build independent alternative models to constitute the model space of Bayesian model aver­ aging (BMA) in groundwater/surface water modeling. Using uniform prior weights can lead to overweighting models with similar structures, as well as biased posterior model weights and BMA predictions. This study applied a correlation matrix R to measure the correlations among alternative models. And two weighting schemes based on R, namely the cos-square (CS) and capped eigenvalue (CE), were used to dilute models’ prior weights. Additionally, the effective model number (Neff) metric derived from R was proposed to measure the effectiveness of BMA model set. Based on two real-world cases (snowmelt runoff modeling and groundwater modeling), and a synthetical groundwater case, we validated the importance of prior weight dilution and the important value of the R-based methods in improving BMA prediction. The results demonstrated that the prior weight dilution schemes redistribute models’ prior weights by penalizing highly correlated models while rewarding those with relatively independent structures. The BMA predictive performance is improved using the weight dilution schemes, with the CS scheme outperforming the CE scheme. In addition, the correlation matrix provides insight into the rationality of the model structures in the BMA model set. The metric of Neff can serve as an effective tool for quantifying the effectiveness of the model set, which provides an important reference for updating the model set and improving BMA predictions with prior weight dilution schemes.