  In this paper we propose to evaluate and compare Markov chain Monte Carlo
(MCMC) methods to estimate the parameters in a generalized extreme value model.
We employed the Bayesian approach using traditional Metropolis-Hastings
methods, Hamiltonian Monte Carlo (HMC) and Riemann manifold HMC (RMHMC) methods
to obtain the approximations to the posterior marginal distributions of
interest. Applications to real datasets of maxima illustrate illustrate how HMC
can be much more efficient computationally than traditional MCMC and simulation
studies are conducted to compare the algorithms in terms of how fast they get
close enough to the stationary distribution so as to provide good estimates
with a smaller number of iterations.
