Μεταπτυχιακές Εργασίες

Μόνιμο URI για αυτήν τη συλλογήhttps://pyxida.aueb.gr/handle/123456789/15

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Adaptive Bayesian variable selection for regression with large number of covariates
Michail, Konstantinos Ion S.; Μιχαήλ, Κωνσταντίνος Ίων Σ.; Athens University of Economics and Business, Department of Statistics; Tsiamyrtzis, Panagiotis; Vasdekis, Vassilis; Ntzoufras, Ioannis
This thesis is an overview of some of the most recent developments on the topic of Bayesian Variable Selection, both from a theoretical and a computational point of view. We turn our attention to objective Bayes methods and discuss their extensions to high-dimensional settings. We also provide a detailed proof of the Unitary Bayes Factor property which was not available. By taking advantage of the closed form expressions of the posterior model distribution (up to a unknown normalizing constant) we employ Adaptive MCMC algorithms to explore the posterior model space. We showcase the ability of Adaptive MCMC to outperform default Metropolis Hastings algorithms for model space exploration such as MC3. We also empirically assess the model selection consistency of Objective Bayes methods, provide examples of variable selection in high dimensional settings as well as how Bayesian Variable selection can be implemented in order to estimate non-linear functions. Our analysis of real datasets shows that the reviewed methods can result in models which have better predictive performance than the full model, in the n > p case and are comparable to the performance of shrinkage priors in high dimensional settings at a lower computational cost.

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Πλοήγηση Μεταπτυχιακές Εργασίες ανά Θέμα "Adaptive MCMC"