  The univariate generalized extreme value (GEV) distribution is the most
commonly used tool for analysing the properties of rare events. The ever
greater utilization of Bayesian methods for extreme value analysis warrants
detailed theoretical investigation, which has thus far been underdeveloped.
Even the most basic asymptotic results are difficult to obtain because the GEV
fails to satisfy standard regularity conditions. Here, we prove that the
posterior distribution of the GEV parameter vector, given an independent and
identically distributed sequence of observations, converges to a normal
distribution centred at the true parameter. The proof necessitates analysing
integrals of the GEV likelihood function over the entire parameter space, which
requires considerable care because the support of the GEV density depends on
the parameters in complicated ways.
