Approaches for bayesian variable selection

Edward I. George, Robert McCulloch

Research output: Contribution to journalArticle

593 Citations (Scopus)

Abstract

This paper describes and compares various hierarchical mixture prior formulations of variable selection uncertainty in normal linear regression models. These include the nonconjugate SSVS formulation of George and McCulloch (1993), as well as conjugate formulations which allow for analytical simplification. Hyperparameter settings which base selection on practical significance, and the implications of using mixtures with point priors are discussed. Computational methods for posterior evaluation and exploration are considered. Rapid updating methods are seen to provide feasible methods for exhaustive evaluation using Gray Code sequencing in moderately sized problems, and fast Markov Chain Monte Carlo exploration in large problems. Estimation of normalization constants is seen to provide improved posterior estimates of individual model probabilities and the total visited probability. Various procedures are illustrated on simulated sample problems and on a real problem concerning the construction of financial index tracking portfolios.

Original languageEnglish (US)
Pages (from-to)339-373
Number of pages35
JournalStatistica Sinica
Volume7
Issue number2
StatePublished - Apr 1997
Externally publishedYes

Fingerprint

Bayesian Variable Selection
Formulation
Gray Code
Selection of Variables
Hyperparameters
Probability Model
Evaluation
Markov Chain Monte Carlo
Linear Regression Model
Computational Methods
Simplification
Sequencing
Normalization
Updating
Uncertainty
Variable selection
Estimate
Financial index
Linear regression model
Markov chain Monte Carlo

Keywords

  • Conjugate prior
  • Gibbs sampling
  • Gray Code
  • Hierarchical models
  • Markov chain Monte Carlo
  • Metropolis-Hastings algorithms
  • Normal mixtures
  • Normalization constant
  • Regression
  • Simulation

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Approaches for bayesian variable selection. / George, Edward I.; McCulloch, Robert.

In: Statistica Sinica, Vol. 7, No. 2, 04.1997, p. 339-373.

Research output: Contribution to journalArticle

George, EI & McCulloch, R 1997, 'Approaches for bayesian variable selection', Statistica Sinica, vol. 7, no. 2, pp. 339-373.
George, Edward I. ; McCulloch, Robert. / Approaches for bayesian variable selection. In: Statistica Sinica. 1997 ; Vol. 7, No. 2. pp. 339-373.
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