title: Variable selection in semi-parametric models.
abstract: We propose Bayesian variable selection methods in semi-parametric models in the framework of partially linear Gaussian and problit regressions. Reproducing kernels are utilized to evaluate possibly non-linear joint effect of a set of variables. Indicator variables are introduced into the reproducing kernels for the inclusion or exclusion of a variable. Different scenarios based on posterior probabilities of including a variable are proposed to select important variables. Simulations are used to demonstrate and evaluate the methods. It was found that the proposed methods can efficiently select the correct variables regardless of the feature of the effects, linear or non-linear in an unknown form. The proposed methods are applied to two real data sets to identify cytosine phosphate guanine methylation sites associated with maternal smoking and cytosine phosphate guanine sites associated with cotinine levels with creatinine levels adjusted. The selected methylation sites have the potential to advance our understanding of the underlying mechanism for the impact of smoking exposure on health outcomes, and consequently benefit medical research in disease intervention.
authors.affiliation: Division of Epidemiology, Biostatistics, and Environmental Health, School of Public Health, University of Memphis, TN, USA hzhang@sc.edu.
authors.forename: Hongmei
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Department of Statistics, North Carolina State University, NC, USA.
authors.forename: Arnab
authors.initials: A
authors.lastname: Maity
authors.affiliation: The David Hide Asthma and Allergy Research Center, St. Marys Hospital, Isle of Wight, UK Allergy and Clinical Immunology, University of Southampton, Southampton, UK.
authors.forename: Hasan
authors.initials: H
authors.lastname: Arshad
authors.affiliation: Faculty of Medicine, University of Southampton, Southampton, UK.
authors.forename: John
authors.initials: J
authors.lastname: Holloway
authors.affiliation: Division of Epidemiology, Biostatistics, and Environmental Health, School of Public Health, University of Memphis, TN, USA.
authors.forename: Wilfried
authors.initials: W
authors.lastname: Karmaus
mesh_terms: D001499:Bayes Theorem; D003367:Cotinine / Q000032:analysis; D018899:CpG Islands; D003404:Creatinine / Q000378:metabolism; D019363:Cytochrome P-450 CYP1A1 / Q000235:genetics; D019175:DNA Methylation; D066264:Datasets as Topic; D004843:Epistasis, Genetic; D005260:Female; D006801:Humans; D016014:Linear Models; D009035:Mothers; D016011:Normal Distribution; D011247:Pregnancy; D012907:Smoking / Q000235:genetics*
chemical_list: D003404:Creatinine; D019363:Cytochrome P-450 CYP1A1; D003367:Cotinine
keywords: Bayesian methods; Gaussian kernel; non-linear effects; partially linear regression; probit regression; reproducing kernel; variable selection