  Using Bayesian methods for extreme value analysis offers an alternative to
frequentist ones, with several advantages such as easily dealing with
parametric uncertainty or studying irregular models. However, computations can
be challenging and the efficiency of algorithms can be altered by poor
parametrization choices. The focus is on the Poisson process characterization
of univariate extremes and outline two key benefits of an orthogonal
parameterization. First, Markov chain Monte Carlo convergence is improved when
applied on orthogonal parameters. This analysis relies on convergence
diagnostics computed on several simulations. Second, orthogonalization also
helps deriving Jeffreys and penalized complexity priors, and establishing
posterior propriety thereof. The proposed framework is applied to return level
estimation of Garonne flow data (France).
