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\begin{document}

\title{Improving Bayesian Model Averaging for Ensemble Flood Modeling Using
Multiple Markov Chains Monte Carlo Sampling}



\author[1]{Tao Huang}%
\author[1]{Venkatesh Mohan Merwade}%
\affil[1]{Purdue University}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\begin{abstract}
As all kinds of physics-based and data-driven models are emerging in
hydrologic and hydraulic engineering, Bayesian model averaging (BMA) is
one of the popular multi-model methods used to account for various
uncertainty sources in the flood modeling process and generate robust
ensemble predictions. The reliability of BMA parameters (weights and
variances) determines the accuracy of BMA predictions. However, the
uncertainty in BMA parameters with fixed values, which are usually
obtained from 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,
Metropolis-Hastings (M-H) algorithm, which is one of the most widely
used algorithms in Markov Chain Monte Carlo (MCMC) method, is proposed
to estimate BMA parameters. Both numerical experiments and
one-dimensional HEC-RAS models are employed to examine the applicability
of M-H algorithm with multiple independent Markov chains. The
performances of EM and M-H algorithms are compared based on the daily
water stage predictions from 10 model members. Results show that BMA
weights estimated from both algorithms are comparable, while BMA
variances obtained from M-H algorithm are closer to the given variances
in the numerical experiment. Moreover, the normal proposal used in M-H
algorithm can yield narrower distributions for BMA weights than those
from the uniform proposal. Overall, MCMC approach with multiple chains
can provide more information associated with the uncertainty of BMA
parameters and its performance is better than the default EM algorithm
in terms of multiple evaluation metrics as well as algorithm
flexibility.%
\end{abstract}%



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\textbf{Hosted file}

\verb`959271_0_art_file_10825080_rry172.docx`  available at \url{https://authorea.com/users/533611/articles/632622-improving-bayesian-model-averaging-for-ensemble-flood-modeling-using-multiple-markov-chains-monte-carlo-sampling}

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