Bayesian methods: ultrahigh dimensional variable selection for generalized linear models and spatiotemporal data modeling
【概要】
Inspired by our recent works on the NSF ATD challenges for spatiotemporal data analysis and modeling and Bayesian clustering research, we investigate whether the Bayesian methods can consistently estimate the model parameters when there are multivariate mixed-type responses. To this end, shrinkage priors are useful for identifying relevant signals in high-dimensional data. 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 posterior consistency and quantifies the posterior contraction rate. We propose a two-step posterior sampling method and prove its efficiency. We provide simulation studies and real-world gene data examples. I will also introduce a novel positron emission tomography (PET) image reconstruction method using both discrete Poisson distributed photon counts and continuous positronium lifetime data.
