Reply to Comment on “Improving Bayesian Model Averaging for Ensemble Flood Modeling Using Multiple Markov Chains Monte Carlo Sampling” by Jasper Vrugt

Abstract

This discussion is a reply to the comments made by Dr. Jasper Vrugt on the Metropolis-Hastings (M-H) algorithm with multiple independent Markov chains proposed by Huang and Merwade (2023a), https://doi.org/10.1029/2023wr034947 concerning the validity of the methodology in estimating Bayesian model averaging (BMA) parameters (weights and variances) of the framework proposed by Raftery et al. (2005), https://doi.org/10.1175/mwr2906.1. In this reply, we address his concerns by emphasizing the motivation of applying the proposed M-H algorithm to BMA analysis and the applicability of the effective sample size that accounts for the autocorrelation across samples in evaluating the efficiency of Markov chain Monte Carlo sampling. Moreover, the details of sampling procedure for BMA prediction distribution are clarified. On the other hand, we present a fair comparison of the default Expectation-Maximization, M-H, and differential evolution adaptive Metropolis (DREAM) algorithms in estimating BMA parameters based on a numerical experiment. Results reinforce the findings obtained from Huang and Merwade (2023a) https://doi.org/10.1029/2023wr034947 and further indicate that the proposed M-H algorithm is better than the DREAM algorithm in terms of sampling efficiency and prediction accuracy. Accordingly, we raise concerns on the use of DREAM algorithm in BMA analysis and suggest conducting peer reviews on the MODELAVG toolbox.