  The univariate generalized extreme value (GEV) distribution is the most
commonly used tool for analyzing 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 $n$ independent and
identically distributed samples, converges in distribution to a trivariate
normal distribution. The proof necessitates analyzing 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.
