A Bayesian framework for Poisson process characterization of extremes with uninformative prior

Théo Moins (1) , Julyan Arbel (1) , Anne Dutfoy (2) , Stéphane Girard (1)

1 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension
2 EDF R&D PERICLES - PERformance et prévention des Risques Industriels du parC par la simuLation et les EtudeS

Combining extreme-value theory with Bayesian methods offers several advantages, such as the availability of posterior predictive inference or the ability to study irregular cases for frequentist statistics. When no prior information is available, objective Bayes aims at using an external rule to construct a prior distribution. In particular, we focus on the use of Jeffreys prior for the Poisson process characterization of extremes, a model which generalizes the two most frequent ones i.e. the extreme-value distribution (EVD) for block-maxima and the generalized Pareto distribution (GPD) for peaks-over-threshold. After showing posterior propriety results, we also compare different reparametrisations of the Poisson process to facilitate sampling by Markov chain Monte Carlo (MCMC). In particular, the influence of a hyperparameter of the model and the interest of parameters orthogonality for Bayesian inference are investigated on simulated data.

Domaines: Statistiques [math.ST]

Théo Moins, Julyan Arbel, Anne Dutfoy, Stéphane Girard. A Bayesian framework for Poisson process characterization of extremes with uninformative prior. CMStatistics 2021 - 14th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2021, London, United Kingdom. ⟨hal-03501794⟩