High dimensional Single Index Bayesian Modeling of the Brain Atrophy over time
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We study the effects of gender, APOE genes, age, genetic variation and Alzheimer's disease on the atrophy of the brain regions. In the real data analysis section, we add a subject specific random effect to capture subject inhomogeneity. A nonparametric single index Bayesian model is proposed to study the data with B-spline series prior on the unknown functions and Dirichlet process scale mixture of zero mean normal prior on the distributions of the random effects. Posterior consistency of the proposed model without the random effect is established for a fixed number of regions and time points with increasing sample size. A new Bayesian estimation procedure for high dimensional single index model is introduced in this paper. Performance of the proposed Bayesian method is compared with the corresponding least square estimator in the linear model with LASSO and SCAD penalization on the high dimensional covariates. The proposed Bayesian method is applied on a dataset of 748 individuals with 620,901 SNPs and 6 other covariates for each individual.
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