Bayesian Frequency Analysis

Abstract

The traditional frequency analysis attempts to fit a specific probability model on the basis of limited data, from which the flood level corresponding to a given return period is determined. Because of: (1) Scatter of observed data about the theoretical probability model; (2) uncertainty of extrapolation from limited measured record; and (3) uncertainty in selecting the correct model, the flood level corresponding to a given return period should be a random variable. Through a Bayesian regression analysis the above uncertainties can be used in evaluating the resulting probability distribution of the flood level. Alternatively, the return period associated with a given flood level may also be treated as a random variable whose distribution can also be evaluated. The model uncertainty may be then incorporated in evaluating hydrologic risk of a system over its expected life time.