Bayesian Inference for Generalized Extreme Value Distributions via Hamiltonian Monte Carlo

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 both traditional Metropolis-Hastings methods and Hamiltonian Monte Carlo (HMC) methods to obtain the approximations to the posterior marginal distributions of interest. An application to a real dataset of maxima illustrates how HMC can be much more efficient computationally than traditional MCMC. A simulation study is conducted to compare the two 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.