Bayesian variable selection with strong heredity constraints

Joungyoun Kim, Johan Lim, Yongdai Kim, Woncheol Jang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we propose a Bayesian variable selection method for linear regression models with high-order interactions. Our method automatically enforces the heredity constraint, that is, a higher order interaction term can exist in the model only if both of its parent terms are in the model. Based on the stochastic search variable selection George and McCulloch (1993), we propose a novel hierarchical prior that fully considers the heredity constraint and controls the degree of sparsity simultaneously. We develop a Markov chain Monte Carlo (MCMC) algorithm to explore the model space efficiently while accounting for the heredity constraint by modifying the shotgun stochastic search algorithm Hans et al. (2007). The performance of the new model is demonstrated through comparisons with other methods. Numerical studies on both real data analysis and simulations show that our new method tends to find relevant variable more effectively when higher order interaction terms are considered.

Original languageEnglish
Pages (from-to)314-329
Number of pages16
JournalJournal of the Korean Statistical Society
Issue number3
StatePublished - Sep 2018


  • Heredity principle
  • Interaction
  • Shotgun stochastic search
  • Strong heredity
  • Variable selection


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