Estimating Bayesian Model Averaging Weights and Variances of Ensemble
Flood Modeling Using Multiple Markov Chains Monte Carlo
Abstract
As all kinds of physics-based and data-driven models are emerging in the
fields of hydrologic and hydraulic engineering, Bayesian model averaging
(BMA) is one of the popular multi-model methods used to account for the
various uncertainty sources in the flood modeling process and generate
robust ensemble predictions based on multiple competitive candidate
models. The reliability of BMA parameters (weights and variances)
determines the accuracy of BMA predictions. However, the uncertainty in
the BMA parameters with fixed values, which are usually obtained from
the Expectation-Maximization (EM) algorithm, has not been adequately
investigated in BMA-related applications over the past few decades.
Given the limitations of the commonly used EM algorithm, the
Metropolis-Hastings (M-H) algorithm, which is one of the most widely
used algorithms in the Markov Chain Monte Carlo (MCMC) method, is
proposed to estimate the BMA parameters and quantify their associated
uncertainty. Both numerical experiments and the one-dimensional HEC-RAS
models are employed to examine the applicability of the M-H algorithm
with multiple independent Markov chains. The performances of the EM and
M-H algorithms in the BMA analysis are compared based on the daily water
stage predictions from 10 model configurations. The results show that
the BMA weights estimated from both algorithms are comparable, while the
BMA variances obtained from the M-H MCMC algorithm are closer to the
given variances in the numerical experiment. Moreover, the normal
proposal distribution used in the M-H algorithm can yield narrower
distributions for the BMA weights than those from the uniform prior.
Overall, the MCMC approach with multiple chains can provide more
information associated with the uncertainty of BMA parameters and its
prediction performance is better than the default EM algorithm in terms
of multiple evaluation metrics as well as algorithm flexibility.