Bayesian MCMC flood frequency analysis with historical information

This paper explores Bayesian Markov Chain Monte Carlo (MCMC) methods for evaluation of the posterior distributions of flood quantiles, flood risk, and parameters of both the log-normal and Log-Pearson Type 3 distributions. Bayesian methods allow a richer and more complete representation of large flood records and historical flood information and their uncertainty (particularly measurement and discharge errors) than is computationally convenient with maximum likelihood and moment estimators. Bayesian MCMC provides a computationally attractive and straightforward method to develop a full and complete description of the uncertainty in parameters, quantiles and performance metrics. Examples illustrate limitations of traditional first-order second-moment analyses based upon the Fisher Information matrix.