Bayesian Inference for Generalized Extreme Value Distributions via Hamiltonian Monte Carlo

TL;DR

This paper compares Bayesian MCMC methods, including Hamiltonian Monte Carlo, for estimating parameters in generalized extreme value models, demonstrating HMC's superior computational efficiency through real data applications and simulation studies.

Contribution

It introduces the use of Hamiltonian Monte Carlo and Riemann manifold HMC for GEV parameter estimation, highlighting their efficiency over traditional methods.

Findings

HMC outperforms Metropolis-Hastings in computational efficiency.

HMC provides accurate posterior estimates with fewer iterations.

Real data applications confirm the practical advantages of HMC.

Abstract

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.