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

Abstract

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.

Keywords

• adaptive metropolis–hastings (am-h) algorithm
• frequency distribution
• markov chain monte carlo (mcmc)
• parameter optimization
• parameter uncertainty analysis
• rainfall frequency modeling