  In this paper, we discuss a method to define prior distributions for the
threshold of a generalised Pareto distribution, in particular when its
applications are directed to heavy-tailed data. We propose to assign prior
probabilities to the order statistics of a given set of observations. In other
words, we assume that the threshold coincides to one of the data points. We
show two ways of defining a prior: by assigning equal mass to each order
statistic, that is a uniform prior, and by considering the worth that every
order statistic has in representing the true threshold. Both proposed priors
represent a scenario of minimal information, and we study their adequacy
through simulation exercises and by analysing two applications from insurance
and from finance.

Methodology