Encoding prior experts judgments to improve risk analysis of extreme hydrological events via POT modeling

One of the main decisions to be made in operational hydrology is to estimate design floods for safety purposes. These floods are generally much rare events that have already been systematically recorded and consequently the results of any estimation process are subject to high levels of uncertainty. When adopting the frequentist framework of probability, the so called ʹrespect of scientific objectivityʹ shall forbid the hydrologists to introduce prior knowledge such as quantified hydrological expertise into the analysis. However, such an expertise can significantly improve the capability of a probabilistic model to extrapolate extreme value events. The Bayesian paradigm offers coherent tools to quantify the prior knowledge of experts. This paper develops an inference procedure for the peak over threshold (POT) model, using semiconjugate informative priors. Such prior structures are convenient to encode a wide variety of prior expertise. They avoid recourse to Monte Carlo Markov Chain techniques which are presently the standard for Bayesian analyses, but such algorithms may be uneasy to implement. We show that prior expertise can significantly reduce uncertainty on design values. Using the Garonne case study with a sample of systematic data spanning over the period 1913-1977, we point out that: (1) the elicitation approach for subjective prior information can be based on quantities with a definite practical hydrological meaning for the expert; (2) with respect to the usual Poisson-Generalized Pareto model, a semi-conjugate prior offers a flexible structure to assess expert knowledge about extreme behavior of the river flows. In addition, it leads to quasi-analytical formulations; (3) tractable algorithms can be implemented to approximate the prior uncertainty about POT parameters into these semi conjugate distribution forms via simple Monte Carlo simulations and normal approximations; (4) the design value and its credible interval are notably changed when incorporating prior knowledge into the risk analysis.