MÃtodo adaptativo de Markov Chain Monte Carlo para manipulaÃÃo de modelos Bayesianos

AUTOR(ES)

Paulo Renato Alves Firmino

DATA DE PUBLICAÇÃO

2009

RESUMO

Historically, Bayesian models have deserved special attention from academy and applied fields mainly by allowing mathematical combination of human judgments and empirical data. Markov Chain Monte Carlo (MCMC) methodology is one of the main classes of approaches for computing marginal estimates from Bayesian models. Among Markov Chain Monte Carlo methods, Metropolis-Hastings algorithms must be emphasized. In summary, for the set of d variables (or components) of the Bayesian model, X = (X1, X2, â, Xd), such algorithm elaborate a Markov Chain where each visited state is a random realization of X, x = (x1, x2, â, xd), sampled from the full conditional distribution of the variables, f(xi| x1, x2, â, xi-1, xi+1, â, xd). When the sampling process is governed by distributions cheap to be sampled from, Metropolis-Hastings algorithm converge towards the well-known Gibbs sampling and variance reduction techniques such as Rao-Blackwellization can be introduced into the inference. Otherwise, in the face of distributions expensive to be sampled from, Rao- Blackwellization is possible by adopting approximate functions and then a griddy-Gibbs sampling approach, originally a non- Metropolis-Hastings extension since eventual rejections are not taken into account. This thesis is an effort for studying griddy-Gibbs sampling as a Metropolis-Hastings variant. In this way, adaptive rejection Metropolis sampling concepts and simple clustering and numerical integration algorithms (like centroidal Voronoi tessellations and adaptive Simpsonâs rule, respectively) are introduced into griddy-Gibbs approach. Case studies from literature point out the good performance of the proposed method in comparison with established methods in terms of both accuracy and time consumption

ASSUNTO(S)

integraÃÃo de monte carlo via cadeias de markov bayesian models mÃtodos de agrupamento engenharia de produÃÃo clustering, rao-blackwellization markov chain monte carlo engenharia de producao rao-blackwellization adaptive quadrature methods mÃtodos de quadratura adaptativos modelos bayesianos

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