Bayesian Variable Selections for Probit Models with Componentwise Gibbs Samplers

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3 Citations (Scopus)

Abstract

This article considers Bayesian variable selection problems for binary responses via stochastic search variable selection and Bayesian Lasso. To avoid matrix inversion in the corresponding Markov chain Monte Carlo implementations, the componentwise Gibbs sampler (CGS) idea is adopted. Moreover, we also propose automatic hyperparameter tuning rules for the proposed approaches. Simulation studies and a real example are used to demonstrate the performances of the proposed approaches. These results show that CGS approaches do not only have good performances in variable selection but also have the lower batch mean standard error values than those of original methods, especially for large number of covariates.

Original languageEnglish
Pages (from-to)2752-2766
Number of pages15
JournalCommunications in Statistics: Simulation and Computation
Volume45
Issue number8
DOIs
Publication statusPublished - 2016 Sep 13

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Bayesian Variable Selection
Probit Model
Gibbs Sampler
Variable Selection
Markov processes
Tuning
Batch Means
Binary Response
Lasso
Stochastic Search
Matrix Inversion
Hyperparameters
Standard error
Markov Chain Monte Carlo
Covariates
Simulation Study
Demonstrate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation

Cite this

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abstract = "This article considers Bayesian variable selection problems for binary responses via stochastic search variable selection and Bayesian Lasso. To avoid matrix inversion in the corresponding Markov chain Monte Carlo implementations, the componentwise Gibbs sampler (CGS) idea is adopted. Moreover, we also propose automatic hyperparameter tuning rules for the proposed approaches. Simulation studies and a real example are used to demonstrate the performances of the proposed approaches. These results show that CGS approaches do not only have good performances in variable selection but also have the lower batch mean standard error values than those of original methods, especially for large number of covariates.",
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AB - This article considers Bayesian variable selection problems for binary responses via stochastic search variable selection and Bayesian Lasso. To avoid matrix inversion in the corresponding Markov chain Monte Carlo implementations, the componentwise Gibbs sampler (CGS) idea is adopted. Moreover, we also propose automatic hyperparameter tuning rules for the proposed approaches. Simulation studies and a real example are used to demonstrate the performances of the proposed approaches. These results show that CGS approaches do not only have good performances in variable selection but also have the lower batch mean standard error values than those of original methods, especially for large number of covariates.

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