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Bayesian Methods for High-dimensiona...

Zhang, Yan.

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Bayesian Methods for High-dimensional Data.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bayesian Methods for High-dimensional Data./
Author:	Zhang, Yan.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	123 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:	Dissertation Abstracts International78-08B(E).
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583617
ISBN:	9781369622966

Bayesian Methods for High-dimensional Data.
Zhang, Yan.

Bayesian Methods for High-dimensional Data. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 123 p.

Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2016.

High-dimensional data arises in multiple fields, such as genetics, finance, medicine, etc. A number of statistical methods have been developed to deal with variable selection in highdimensional linear models. In this thesis, we propose several new Bayesian methods to address such problems. Chapter 1 presents a selective literature review of existing statistical methods with a main focus on Bayesian variable selection methodologies. A selective review of recommender systems are also given in this chapter.

ISBN: 9781369622966Subjects--Topical Terms:

517247
Statistics.

Bayesian Methods for High-dimensional Data.
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245 1 0 $a Bayesian Methods for High-dimensional Data.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 123 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
500 $a Adviser: Howard D. Bondell.
502 $a Thesis (Ph.D.)--North Carolina State University, 2016.
520 $a High-dimensional data arises in multiple fields, such as genetics, finance, medicine, etc. A number of statistical methods have been developed to deal with variable selection in highdimensional linear models. In this thesis, we propose several new Bayesian methods to address such problems. Chapter 1 presents a selective literature review of existing statistical methods with a main focus on Bayesian variable selection methodologies. A selective review of recommender systems are also given in this chapter.
520 $a Chapter 2 proposes a Bayesian variable selection method by incorporating global-local priors into the credible region selection framework, which separates model fitting and variable selection, to search for the sparsest solution within the joint posterior credible regions. The Dirichlet-Laplace (DL) prior is adapted to linear regression. Posterior consistency for the normal and DL priors is shown, along with variable selection consistency. We also introduce a new method to tune hyperparameters in prior distributions for linear regression. We propose to choose the hyperparameters to minimize a discrepancy between the induced distribution on R-square and a prespecified target distribution. Prior elicitation on R-square is more natural, particularly when there are a large number of predictor variables in which elicitation on that scale is not feasible. For a normal prior, these hyperparameters are available in closed form to minimize the Kullback-Leibler divergence between the distributions.
520 $a Chapter 3 proposes a new class of priors for linear regression, the R-square induced Dirichlet Decomposition (R2-D2) prior. The prior is induced by a Beta prior on the coefficient of determination, and then the total prior variance of the regression coefficients is decomposed through a Dirichlet prior. We demonstrate both theoretically and empirically the advantages of the R2-D2 prior over a number of common shrinkage priors, including the Horseshoe, Horseshoe+, and Dirichlet-Laplace priors. The R2-D2 prior possesses the fastest concentration rate around zero and heaviest tails among these common shrinkage priors, which is established based on its marginal density, a Meijer G-function. We show that its Bayes estimator converges to the truth at a Kullback-Leibler super-efficient rate, attaining a sharper information theoretic bound than existing common shrinkage priors. We also demonstrate that the R2-D2 prior yields a consistent posterior. The R2-D2 prior permits straightforward Gibbs sampling and thus enjoys computational tractability. The proposed prior is further investigated in a mouse gene expression application.
520 $a Chapter 4 is motivated by a movie rating system. This chapter proposes a full Bayesian hybrid recommender system, using a shared-variable approach for matrix completion to coerce informative missingness into a regression-based model to improve prediction performance. We jointly model the movie rating and the probability of each movie being rated as a function of the expected rating. The proposed model is fitted through MCMC sampling. The computation is stable, accurate and easy to implement. We apply our model on a movie rating system, particularly the MovieLens data. Our method illustrates significant improvement in prediction by adding informative missingness into the model.
590 $a School code: 0155.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 $a North Carolina State University. $3 1018772
773 0 $t Dissertation Abstracts International $g 78-08B(E).
790 $a 0155
791 $a Ph.D.
792 $a 2016
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583617