BAYESIAN ESTIMATION OF QUANTILES FOR THE PURPOSE OF FLOOD PREVENTION

J.M. van Noortwijk, P.H.A.J.M. van Gelder

Abstract


In this paper, the problem of Bayesian estimation of flood quantiles is studied. Bayes estimators of the optimal dyke height under symmetric and asymmetric loss are investigated when the annual maximum sea water levels are exponentially distributed with unknown value of the mean. Three types of loss functions are considered: (i) linear loss, (ii) squared-error loss, and (iii) linex loss. In order to properly account for the statistical uncertainty in the mean, a modified linex loss function is to be preferred. This new modified linex loss function is derived from the economic dyke heigthening problem of Van Dantzig. Since the loss function is based on a benefit-cost analysis, its parameters have a clear economic significance.

Keywords


flood prevention; Bayesian estimation; quantile

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