  The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions
play an important role in extreme value analyses, as models for threshold
excesses and block maxima respectively. For each of these distributions we
consider Bayesian inference using "reference" prior distributions (in the
general sense of priors constructed using formal rules) for the model
parameters, specifically a Jeffreys prior, the maximal data information (MDI)
prior and independent uniform priors on separate model parameters. We
investigate the important issue of whether these improper priors lead to proper
posterior distributions. We show that, in the GP and GEV cases, the MDI prior,
unless modified, never yields a proper posterior and that in the GEV case this
also applies to the Jeffreys prior. We also show that a sample size of three
(four) is sufficient for independent uniform priors to yield a proper posterior
distribution in the GP (GEV) case.
