Abstract
It is valuable to construct likelihood functions that rigorously incorporate measurement errors and annual peak discharge, historical, and paleohydrologic bound information in Bayesian flood frequency analyses. Estimates of primary posterior modes for common three‐parameter frequency distributions are constructed using simulated annealing and the simplex method. Parameter and flood frequency probability intervals are calculated directly by systematic parameter space integration. Bayesian flood frequency analyses with annual peak discharge, historical, and paleohydrologic bound data for the Santa Ynez River, California, and the Big Lost River, Idaho, demonstrate that paleohydrologic bounds reduce quantile biases by placing large observed peak discharges in their proper long‐term contexts and substantially narrow peak discharge confidence intervals when estimating floods with low exceedance probabilities.
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