Nonlocal priors for Bayesian variable selection in generalized linear models and generalized linear mixed models and their applications in biology data

Abstract

A crucial problem in building a generalized linear model (GLM) or a generalized linear mixed model (GLMM) is to identify which subset of predictors should be included into the model. Hence, the main thrust of this dissertation is aimed to discuss and showcase our promising Bayesian methods that circumvent this problem in both GLMs and GLMMs. In the first part of the dissertation, we study the hyper-g prior based Bayesian variable selection procedure for generalized linear models. In the second part of the dissertation, we propose two novel scale mixtures of nonlocal priors (SMNP) for variable selection in GLMs. In the last part of the dissertation, we develop novel nonlocal prior for variable selection in generalized linear mixed models (GLMM) and apply the proposed nonlocal prior and its inference procedure for the whole genome allelic imbalance detection.