Date of Completion

6-15-2016

Embargo Period

6-15-2016

Keywords

Bayesian model selection; Conditional marginal density estimator; Cure rate model; Harmonic mean estimator; Inflated density ratio estimator; Ordinal probit regression; Power prior; Savage-Dickey density ratio; Stepping-stone method; Variable tree topology.

Major Advisor

Professor Lynn Kuo

Co-Major Advisor

Professor Ming-Hui Chen

Associate Advisor

Professor Paul O. Lewis

Associate Advisor

See above

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

This dissertation mainly focuses on the development of new Monte Carlo estimators for marginal likelihood and marginal posterior density with minimal assumptions of a known nonnormalized posterior density and a single MCMC sample from the posterior distribution. We use the ideas of partitioning the parameter space and assigning an adaptive weight to the points of MCMC sample within different partition subsets. The estimators are shown to be consistent with the targets and their optimal performances in terms of minimizing the variance of estimators can be achieved by increasing the number of partition subsets. The proposing methods provide efficient ways to the problems including but not limited to Bayesian model or variable selection, the choices of power prior by empirical Bayes method, and phylogenetic model selection for a variable topology. Moreover, when multiple MCMC samples are available from the posterior density and conditional posterior densities, we provide a hybrid method, which is benefited from the dimension reduction.

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