Parameter optimization and uncertainty assessment for rainfall frequency modeling using an adaptive Metropolis-Hastings algorithm

A new parameter optimization and uncertainty assessment procedure using the Bayesian inference with an adaptive Metropolis-Hastings (AM-H) algorithm is presented for extreme rainfall frequency modeling. An efficient Markov chain Monte Carlo sampler is adopted to explore the posterior distribution of...

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Bibliographic Details
Published in:Water science and technology 2021-03, Vol.83 (5), p.1085-1102
Main Authors: Liu, Xingpo, Xia, Chengfei, Tang, Yifan, Tu, Jiayang, Wang, Huimin
Format: Article
Language:English
Subjects:
Adaptive algorithms
adaptive metropolis–hastings (am-h) algorithm
Algorithms
Approximation
Bayes Theorem
Bayesian analysis
Bayesian theory
China
Cities
Computer Simulation
Estimates
Extreme weather
Frequency distribution
Intervals
Markov analysis
markov chain monte carlo (mcmc)
Markov Chains
Mathematical models
Maximum likelihood estimation
Methods
Modelling
Monte Carlo Method
Optimization
Parameter estimation
parameter optimization
Parameter uncertainty
parameter uncertainty analysis
Precipitation
Probability distribution
Probability theory
Procedures
Quantiles
Rainfall
rainfall frequency modeling
Random variables
Risk assessment
Statistical inference
Statistical methods
Storm runoff
Storms
Uncertainty
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Summary:A new parameter optimization and uncertainty assessment procedure using the Bayesian inference with an adaptive Metropolis-Hastings (AM-H) algorithm is presented for extreme rainfall frequency modeling. An efficient Markov chain Monte Carlo sampler is adopted to explore the posterior distribution of parameters and calculate their uncertainty intervals associated with the magnitude of estimated rainfall depth quantiles. Also, the efficiency of AM-H and conventional maximum likelihood estimation (MLE) in parameter estimation and uncertainty quantification are compared. And the procedure was implemented and discussed for the case of Chaohu city, China. Results of our work reveal that: (i) the adaptive Bayesian method, especially for return level associated to large return period, shows better estimated effect when compared with MLE; it should be noted that the implementation of MLE often produces overy optimistic results in the case of Chaohu city; (ii) AM-H algorithm is more reliable than MLE in terms of uncertainty quantification, and yields relatively narrow credible intervals for the quantile estimates to be instrumental in risk assessment of urban storm drainage planning.
ISSN:0273-1223
1996-9732
DOI:10.2166/wst.2021.032