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  • Research Article
  • Open Access

Variable Selection by Perfect Sampling

EURASIP Journal on Advances in Signal Processing20022002:130194

  • Received: 31 July 2001
  • Published:


Variable selection is very important in many fields, and for its resolution many procedures have been proposed and investigated. Among them are Bayesian methods that use Markov chain Monte Carlo (MCMC) sampling algorithms. A problem with MCMC sampling, however, is that it cannot guarantee that the samples are exactly from the target distributions. This drawback is overcome by related methods known as perfect sampling algorithms. In this paper, we propose the use of two perfect sampling algorithms to perform variable selection within the Bayesian framework. They are the sandwiched coupling from the past (CFTP) algorithm and the Gibbs coupler. We focus our attention to scenarios where the model coefficients and noise variance are known. We indicate the condition under which the sandwiched CFTP can be applied. Most importantly, we design a detailed scheme to adapt the Gibbs coupler algorithm to variable selection. In addition, we discuss the possibilities of applying perfect sampling when the model coefficients and noise variance are unknown. Test results that show the performance of the algorithms are provided.


  • variable selection
  • Markov chain Monte Carlo
  • the Gibbs sampler
  • perfect sampling
  • coupling from the past
  • the Gibbs coupler

Authors’ Affiliations

Department of Electrical and Computer Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794-2350, USA


© Huang and Djurić 2002