Proposta e AvaliaÃÃo de CritÃrios de ConvergÃncia para o MÃtodo de Monte Carlo via Cadeias de Markov: Casos Uni e Multivariados. / Proposal and evaluation of convergence diagnostics criterion for Markov Chain Monte Carlo methods: univariate and multivariate cases.

AUTOR(ES)

Denismar Alves Nogueira

DATA DE PUBLICAÇÃO

2004

RESUMO

Markov Chain Monte Carlo Methods have been studied in several areas, but one of the largest difficulties is to determine the appropriate sample size, i.e., to determine the convergence of the process and then make inference over parameters of the target distribution. In spite of several accessible convergence diagnostic procedures in literature we have opted to study the most used and simplest to implement diagnostic procedures. The objectives of this work were: to propose an alternative form of combined application of 4 univariate Markov chain convergence diagnostics (Gelman &Rubin, 1992a, Raftery &Lewis, 1992a, Geweke, 1992, Heidelberger &Welch, 1983) and optimize their properties; to present an alternative numerical method for calculating the Brooks &Gelmanâs (1998) convergence diagnostic procedure; and to propose two new multivariate convergence diagnostic procedures. Simulated data from two models was used. The first a time series with two intervention parameters with ARMA {2,2} error and the second a normal trivariate, utilizing three different structures for the covariance matrix. In both cases the Gibbs sampler was used. The following conclusions were obtained: it was suggest that univariate diagnostic procedures should be applied in a combined way; the alternative form for calculating Brooks &Gelmanâs convergence diagnostic procedure was easy to be applied and numerically robust; the two new multivariate convergence diagnostics were proposed with success; the multivariate convergence diagnostic based on ratio of the and D covariance matrix traces was considered the best.

ASSUNTO(S)

correlaÃÃo correlation estatistica sÃries temporais time series amostrador de gibbs gibbs sampler

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