Bayesian POT modeling for historical data Eric Parent * , Jacques Bernier GRESE (Laboratory for Risk Analysis in Water Sciences), ENGREF, 19, Avenue du Maine, F-75732 Paris Cedex 15, France Received 4 December 2001; revised 4 November 2002; accepted 15 November 2002 Abstract When designing hydraulic structures, civil engineers have to evaluate design floods, i.e. events generally much rarer that the ones that have already been systematically recorded. To extrapolate towards extreme value events, taking advantage of further information such as historical data, has been an early concern among hydrologists. Most methods described in the hydrological literature are designed from a frequentist interpretation of probabilities, although such probabilities are commonly interpreted as subjective decisional bets by the end user. This paper adopts a Bayesian setting to deal with the classical Poisson–Pareto peak over treshold (POT) model when a sample of historical data is available. Direct probalistic statements can be made about the unknown parameters, thus improving communication with decision makers. On the Garonne case study, we point out that twelve historical events, however imprecise they might be, greatly reduce uncertainty. The 90% credible interval for the 1000 year flood becomes 40% smaller when taking into account historical data. Any kind of uncertainty (model uncertainty, imprecise range for historical events, missing data) can be incorporated into the decision analysis. Tractable and versatile data augmentation algorithms are implemented by Monte Carlo Markov Chain tools. Advantage is taken from a semi-conjugate prior, flexible enough to elicit expert knowledge about extreme behavior of the river flows. The data augmentation algorithm allows to deal with imprecise historical data in the POT model. A direct hydrological meaning is given to the latent variables, which are the Bayesian keytool to model unobserved past floods in the historical series. q 2003 Elsevier Science B.V. All rights reserved. Keywords: Bayesian models; Markov Chain Monte Carlo methods; Gibbs sampling; Data augmentation; Extreme value theory; Flood design; Historical information; Semi-conjugate prior 1. Introduction In a recent survey, Berger (1999) emphasized the very large development of Bayes ideas and appli- cations in the technical literature of many applied domains during the last 10 years. Berger argued that methodological developments are made possible through the use of Monte Carlo Markov Chains simulation techniques and that we are likely to see growth in application of Bayesian ideas for this reason (if no other). Strangely enough, hydrometeorological studies are poorly represented in this survey. For risk analyses of extreme environmental events for instance, with some exceptions such as Kuczera (1999), significant contributions such as Coles and Powell (1996) or Coles and Tawn (1996), have mostly been published in statistical reviews, and did not hold the attention of hydrologists. The Bayesian paradigm allows to revisit many old hydrological problems 0022-1694/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-1694(02)00396-7 Journal of Hydrology 274 (2003) 95–108 www.elsevier.com/locate/jhydrol * Corresponding author. E-mail addresses: parent@engref.fr (E. Parent), jacques. bernier2@wanadoo.fr (J. Bernier).