High-dimensional single-index Bayesian modeling of brain atrophy

TL;DR

This paper introduces a high-dimensional Bayesian model for analyzing brain atrophy, integrating genetic and covariate data, with efficient computation and demonstrated application on a large dataset.

Contribution

It develops a novel nonparametric single-index Bayesian model with advanced priors and efficient HMC sampling for high-dimensional genetic data analysis.

Findings

The model accurately identifies genetic and covariate factors associated with brain atrophy.

Posterior contraction rates are established for fixed regions and time points.

The Bayesian approach outperforms traditional linear models with penalization methods.

Abstract

We propose a model of brain atrophy as a function of high-dimensional genetic information and low dimensional covariates such as gender, age, APOE gene, and disease status. A nonparametric single-index Bayesian model of high dimension is proposed to model the relationship with B-spline series prior on the unknown functions and Dirichlet process scale mixture of centered normal prior on the distributions of the random effects. The posterior rate of contraction without the random effect is established for a fixed number of regions and time points with increasing sample size. We implement an efficient computation algorithm through a Hamiltonian Monte Carlo (HMC) algorithm. The performance of the proposed Bayesian method is compared with the corresponding least square estimator in the linear model with horseshoe prior, LASSO and SCAD penalization on the high-dimensional covariates. The proposed Bayesian method is applied to a dataset on volumes of brain regions recorded over multiple visits of 748 individuals using 620,901 SNPs and 6 other covariates for each individual, to identify factors associated with brain atrophy.