Date of Graduation

7-2020

Document Type

Thesis

Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level

Graduate

Department

Graduate School

Advisor

Jyotishka Datta

Committee Member

Avishek Chakraborty

Second Committee Member

Giovanni Petris

Keywords

Dirichlet-Multinomial regression, Horseshoe, Horseshoe plus, Laplace, Microbiome data, Overdispersion, Variable selection

Abstract

We propose a Bayesian approach to the Dirichlet-Multinomial (DM) regression model, which uses horseshoe, Laplace, and horseshoe plus priors for shrinkage and selection. The Dirichlet-Multinomial model can be used to find the significant association between a set of available covariates and taxa for a microbiome sample. We incorporate the covariates in a log-linear regression framework. We design a simulation study to make a comparison among the performance of the three shrinkage priors in terms of estimation accuracy and the ability to detect true signals. Our results have clearly separated the performance of the three priors and indicated that the horseshoe plus prior outperforms both horseshoe and Laplace priors under low dependence for the compositional data model in the Dirichlet-Multinomial regression framework. We have also seen that heavy dependence among the covariates reduces the rate of variable selection and deteriorates the estimation errors compared to low dependence.

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