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Regression Model Stochastic Search via Local Orthogonalization

Xu, Ruoxi
http://rave.ohiolink.edu/etdc/view?acc_num=osu1322589253

Abstract Details

2011, Doctor of Philosophy, Ohio State University, Statistics.
The Bayesian approach to variable selection has become increasingly popular in high dimensional problems for the reason of being able to incorporate model uncertainty into the analysis. This dissertation reviews a variety of conjugate and non-conjugate prior setups for the Bayesian model uncertainty problem with a particular focus on the point mass prior settings that allow literal exclusion of certain predictors from the model. Stochastic search algorithms for the purpose of exploring the model space, such as Markov chain Monte Carlo methods, need to be implemented carefully under point mass prior settings to ensure proper convergence and fast exploration. Motivated by the difficulty with the Gibbs sampler in making efficient moves in the model space under severe multicollinearity, this dissertation presents a locally orthogonalized Metropolis-Hastings algorithm (LOMH) for the point mass prior settings, that utilizes orthonormal rotations in the parametrization of the model to facilitate the model space exploration. This algorithm samples from the joint parameter-model space, and therefore works under both conjugate and non-conjugate prior setups. Two important variants of LOMH are also introduced in an effort to further improve its efficiency in exploring the model space. The performances of LOMH and two of its variants are illustrated through comparisons with other popular Markov chain Monte Carlo methods under conjugate and non-conjugate setups. Several simulated data sets are used to study their performances in various situations and an example concerning protein activity is employed to test their performances in high dimensional problems.
Christopher Hans, PhD (Advisor)
Steve MacEachern, PhD (Committee Member)
Xinyi Xu, PhD (Committee Member)
Bayesian; Model Uncertainty; MCMC; Orthogonal Rotation

Recommended Citations

Citations

  • Xu, R. (2011). Regression Model Stochastic Search via Local Orthogonalization [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1322589253

    APA Style (7th edition)

  • Xu, Ruoxi. Regression Model Stochastic Search via Local Orthogonalization. 2011. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1322589253.

    MLA Style (8th edition)

  • Xu, Ruoxi. "Regression Model Stochastic Search via Local Orthogonalization." Doctoral dissertation, Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1322589253

    Chicago Manual of Style (17th edition)

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© 2011, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.