Probabilistic design of river dikes is usually based on estimates of a design discharge. Dutch design discharges are currently estimated using classical statistical methods. A shortcoming of this approach is that statistical uncertainties are not taken into account and that probability distributions are given equal weight. In the paper, a method based on Bayesian statistics is presented. Seven probability distributions for annual maxima are investigated for determining extreme quantiles of discharges: the exponential, Rayleigh, normal, log-normal, gamma, Weibull, and Gumbel. Bayes factors are used to determine weights corresponding to how well a probability distribution fits the observed data. Predictive exceedance probabilities are obtained using two different Bayesian computation methods: numerical integration and Markov Chain Monte Carlo (MCMC). MCMC methods can be used to draw samples from the posterior density. The pros and cons of numerical integration and MCMC are given and illustrated by estimating the discharge of the river Rhine with an average return period of 1,250 years.
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