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Title: Ultrahigh dimensional variable selection for Bayesian mixed type multivariate generalized linear models Authors:  Hsin-Hsiung Huang - University of Central Florida (United States) [presenting]
Shao-Hsuan Wang - National Central University (Taiwan)
Ray Bai - University of South Carolina (United States)
Abstract: In recent years, the literature on Bayesian high-dimensional variable selection has rapidly grown. It is increasingly important to understand whether these Bayesian methods can consistently estimate the model parameters. To this end, we develop a multivariate Bayesian model with shrinkage priors (MBSP) model to mixed-type response generalized linear models (MRGLMs), and we consider a latent multivariate linear regression model associated with the observable mixed-type response vector through its link function. Under our proposed model (MBSP-GLM), multiple responses belonging to the exponential family are simultaneously modeled and mixed-type responses are allowed. We show that the MBSP-GLM model achieves strong posterior consistency when p grows at a subexponential rate with $n$. Furthermore, we quantify the posterior contraction rate at which the posterior shrinks around the true regression coefficients and allow the dimension of the responses $q$ to grow as $n$ grows. This greatly expands the scope of the MBSP model to include response variables of many data types, including binary and count data. To address the non-conjugacy concern, we propose an adaptive sampling algorithm via a Polya-gamma data augmentation scheme for the MRGLM estimation. We provide simulation studies and real data examples.