Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


30680.pdf (1.5 MB)

ETD Abstract Container

Abstract Header

On Bayesian Multiplicity Adjustment in Multiple Testing

Gecili, Emrah
http://orcid.org/0000-0001-5221-4922
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1542724883394512

Abstract Details

2018, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
Multiplicity is a common problem in multiple testing for both frequentist and Bayesian approaches. This thesis considers Bayesian approach to the multiple testing problem for different types of data. The first chapter explains the problem of multiple testing and provides backgrounds of both frequentist and Bayesian solutions. Chapter 2 investigates Bayesian multiple testing procedure for two-groups model for independent and normally distributed data. First, we provide results from a simulation-based evaluation of the frequentist features of the Bayesian approach to multiple testing in a variety of scenarios. In the absence of a specified loss function, we suggest the use of frequentist error rates to determine a suitable cut-off for the posterior probability to make a decision about a null. We then introduce a loss function that may be useful when sparsity is deemed desirable. This sparsity inducing loss function (SIL) can be thought of as a modified version of the usual 0-1 loss. It assigns a smaller loss for non-discovery when the signal is close to zero; it is bounded and is computationally similar to 0-1 loss. A numerical comparison of the performance of SIL with the 0-1 loss, absolute error loss, and with some frequentist approaches is carried out by using simulated and real data. Additionally, an empirical Bayes approach is used with SIL and compared with the procedures given in Malgorzata et al. (2007) using simulation. The third chapter examines the objective Bayesian multiple testing approach for discrete independent data. We consider simultaneous testing of multiple null hypotheses concerning two proportions under different settings using Bayesian approach. We use an intrinsic prior with different choices of priors for the training sample size and a mode-based Beta prior. We use simulated and real data sets to compare the results obtained by using these priors. Later, we consider Empirical Bayes procedures for both the intrinsic and Beta priors that can be good approximations for the Fully Bayesian approaches. Additionally, the results from the Bayesian approaches are compared with those of certain commonly used frequentist procedures using simulations and real data sets. Chapter 4 further generalizes multiple testing problem for dependent discrete data. We take into account the correlation between the proportions (response rates) by utilizing from the conditional autoregressive (CAR) type prior in control group to get a better control for multiplicity problem by using appropriate priors. We perform some simulations to study some frequentist features of the proposed procedure with suggested priors. The proposed Bayesian approach is shown to have some advantages when compared with a Bayesian procedure that ignores the correlation and some certain frequentist methods.
Siva Sivaganesan, Ph.D. (Committee Chair)
Hang Joon Kim, Ph.D. (Committee Member)
Bledar Konomi, Ph.D. (Committee Member)
Seongho Song, Ph.D. (Committee Member)
Xia Wang, Ph.D. (Committee Member)
169 p.
Statistics
multiplicity adjustment; multiple testing; bayesian

Recommended Citations

Citations

  • Gecili, E. (2018). On Bayesian Multiplicity Adjustment in Multiple Testing [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1542724883394512

    APA Style (7th edition)

  • Gecili, Emrah. On Bayesian Multiplicity Adjustment in Multiple Testing. 2018. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1542724883394512.

    MLA Style (8th edition)

  • Gecili, Emrah. "On Bayesian Multiplicity Adjustment in Multiple Testing." Doctoral dissertation, University of Cincinnati, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1542724883394512

    Chicago Manual of Style (17th edition)

ucin1542724883394512
165
© 2018, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.