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Statistics and Probability

Theses and Dissertations

Theses/Dissertations

2023

Dependence structure

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Bayesian Dependence Structure Analysis For Ordinal Data, Yang He Apr 2023

Bayesian Dependence Structure Analysis For Ordinal Data, Yang He

Theses and Dissertations

This dissertation explores different methods to study the dependence structure among many ordinal variables under the Bayesian framework.

Chapter 1 introduces ordinal data analysis methods, and the related literature works are briefly reviewed. An outline of the dissertation is put forward.

In Chapter 2, Gaussian copula graphical models with different priors of graphical Lasso, adaptive graphical Lasso, and spike-and-slab Lasso on the precision matrix are assessed and compared. The proposed models are well illustrated via simulations and a real ordinal survey data analysis.

In Chapter 3, adaptive spike-and-slab Lasso prior is proposed as an extension of Chapter 2. The developed …