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On Multiplicity Adjustment in Bayesian Variable Selection and An Objective Bayesian Analysis of a Crossover Design

Li, Dandan
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1396453837

Abstract Details

2014, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
Multiplicity is a common problem in multiple testing for both traditional and Bayesian approaches. The first part of this dissertation considers certain issues relating to multiplicity adjustment in the Bayesian approach. Scott and Berger (2010) explained how multiplicity adjustment is achieved in fully Bayesian approach for model selection by using a single prior on inclusion probability in terms of model prior odds ratio. We extend their work by studying the general properties of model prior odds ratio and using it to propose a measure to quantify the multiplicity adjustment induced by a prior in fully Bayesian framework. Simulation studies are performed to evaluate the proposed measure. Estimation and testing hypotheses about the treatment effects in a crossover design is interesting as it involves consideration whether the carryover effect is present or not. Presence or absence of carryover effect also may depend on the existence of treatment effect. In the second part of this dissertation, we consider a crossover design with normally distributed response variable, and use standard objective priors for estimation and model selection to estimate the treatment effect, and test hypothesis about it. The performance is evaluated by simulation studies through MSE and coverage probability of confidence interval. We apply the approach to a real data example and compare the numerical results with other frequentist and Bayesian approaches.
Siva Sivaganesan, Ph.D. (Committee Chair)
Lei Kang, Ph.D. (Committee Member)
Seongho Song, Ph.D. (Committee Member)
Xia Wang, Ph.D. (Committee Member)
220 p.
Statistics
multiplicity adjustment; variable selection; objective Bayesian; crossover design

Recommended Citations

Citations

  • Li, D. (2014). On Multiplicity Adjustment in Bayesian Variable Selection and An Objective Bayesian Analysis of a Crossover Design [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1396453837

    APA Style (7th edition)

  • Li, Dandan. On Multiplicity Adjustment in Bayesian Variable Selection and An Objective Bayesian Analysis of a Crossover Design. 2014. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1396453837.

    MLA Style (8th edition)

  • Li, Dandan. "On Multiplicity Adjustment in Bayesian Variable Selection and An Objective Bayesian Analysis of a Crossover Design." Doctoral dissertation, University of Cincinnati, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1396453837

    Chicago Manual of Style (17th edition)

ucin1396453837
356
© 2014, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.