Nearly optimal Bayesian shrinkage for high-dimensional regression

During the past decade,shrinkage priors have received much attention in Bayesian analysis of high-dimensional data.This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,which has a heavy and flat tail and allocates a sufficiently large probability mass in a very small neighborhood of zero.While enjoying its efficiency in posterior simulations,the shrinkage prior can lead to a nearly optimal posterior contraction rate and the variable selection consistency as the spike-and-slab prior.Our numerical results show that under the posterior consistency,Bayesian methods can yield much better results in variable selection than the regularization methods such as LASSO and SCAD.This paper also establishes a BvM-type result,which leads to a convenient way of uncertainty quantification for regression coefficient estimates.

Bayesian Peak Picking for NMR Spectra

Protein structure determination is a very important topic in structural genomics,which helps people to understand varieties of biological functions such as protein-protein interactions,protein-DNA interactions and so on.Nowadays,nuclear magnetic resonance （NMR） has often been used to determine the three-dimensional structures of protein in vivo.This study aims to automate the peak picking step,the most important and tricky step in NMR structure determination.We propose to model the NMR spectrum by a mixture of bivariate Gaussian densities and use the stochastic approximation Monte Carlo algorithm as the computational tool to solve the problem.Under the Bayesian framework,the peak picking problem is casted as a variable selection problem.The proposed method can automatically distinguish true peaks from false ones without preprocessing the data.To the best of our knowledge,this is the first effort in the literature that tackles the peak picking problem for NMR spectrum data using Bayesian method.