Comparação de estratégias de geração de propostas no algoritmo Metropolis-Hastings para um modelo Poisson log-linear

Abstract

The Markov Chain Monte Carlo methods (MCMC) are a class of simulation algorithms widely used in Bayesian inference to indirectly draw samples from the posterior distribution, which is known up to a constant of proportionality. The random walk Metropolis- Hastings algorithm is a popular case providing good posterior estimates if the covariance matrix of the proposal distribution is well specied. In high dimensional situations, the specification of this matrix is not trivial. This dissertation aims to carry out comparisons between dierent strategies to generate candidates through Metropolis-Hastings algorithms, that basically dier in terms of the choice of covariance matrix of the proposaldistribution. Adaptive and non-adaptive algorithms are considered. The comparison is made through a simulation study and an analysis of real data set using a Poisson log-linear model with longitudinal count structure. The criteria used to evaluate the performance of the algorithms are: the eective sample size, which is a function of the chain's autocorrelation, and the accuracy of the posterior point and interval estimates. In general, numerical results show that the algorithms estimate well the parameters of interest and they dier with respect to the mixing of the chains and to the computational time, especially the adaptive cases: Adaptive Metropolis, Robust Adaptive Metropolisand Iterative Weighted Least Squares Metropolis.