Bayesian high-dimensional screening via MCMC

Zuofeng Shang, Ping Li

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We explore the theoretical and numerical properties of a fully Bayesian model selection method in the context of sparse high-dimensional settings, i.e., p≫n, where p is the number of covariates and n is the sample size. Our method consists of (1) a hierarchical Bayesian model with a novel prior placed over the model space which includes a hyperparameter tn controlling the model size and (2) an efficient MCMC algorithm for automatic and stochastic search of the models. Our theory shows that, when specifying tn correctly, the proposed method yields selection consistency, i.e., the posterior probability of the true model asymptotically approaches one; when tn is misspecified, the selected model is still asymptotically nested in the true model. The theory also reveals insensitivity of the selection result with respect to the choice of tn. In implementations, a reasonable prior is further assumed on tn. Our approach conducts selection, estimation and even inference in a unified framework. No additional prescreening or dimension reduction step is needed. Two novel g-priors are proposed to make our approach more flexible. The numerical advantages of the proposed approach are demonstrated through comparisons with sure independence screening (SIS).

Original languageEnglish (US)
Pages (from-to)54-78
Number of pages25
JournalJournal of Statistical Planning and Inference
StatePublished - Dec 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Constrained blockwise Gibbs sampler
  • Fully Bayesian method
  • Generalized Zellner-Siow prior
  • Generalized hyper-g prior
  • High-dimensionality
  • Model selection
  • Posterior consistency
  • Size-control prior on model space


Dive into the research topics of 'Bayesian high-dimensional screening via MCMC'. Together they form a unique fingerprint.

Cite this