### Abstract

Bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models, specifying a prior distribution on the model space and computations. We address these three issues for the logistic regression model. For the first, we propose an informative prior distribution for variable selection. Several theoretical and computational properties of the prior are derived and illustrated with several examples. For the second, we propose a method for specifying an informative prior on the model space, and for the third we propose novel methods for computing the marginal distribution of the data. The new computational algorithms only require Gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models. Several properties of the algorithms are also derived. The prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction y_{0} for the response vector and a quantity a_{0} quantifying the uncertainty in y_{0}. Then, y_{0} and a_{0} are used to specify a prior for the regression coefficients semi-automatically. Examples using real data are given to demonstrate the methodology.

Original language | English (US) |
---|---|

Pages (from-to) | 223-242 |

Number of pages | 20 |

Journal | Journal of the Royal Statistical Society. Series B: Statistical Methodology |

Volume | 61 |

Issue number | 1 |

State | Published - 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Gibbs sampling
- Logistic regression
- Normal prior
- Posterior distribution
- Prior distribution
- Selection of variables

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Journal of the Royal Statistical Society. Series B: Statistical Methodology*,

*61*(1), 223-242.

**Prior elicitation, variable selection and Bayesian computation for logistic regression models.** / Chen, Ming Hui; Ibrahim, Joseph G.; Yiannoutsos, Constantin.

Research output: Contribution to journal › Article

*Journal of the Royal Statistical Society. Series B: Statistical Methodology*, vol. 61, no. 1, pp. 223-242.

}

TY - JOUR

T1 - Prior elicitation, variable selection and Bayesian computation for logistic regression models

AU - Chen, Ming Hui

AU - Ibrahim, Joseph G.

AU - Yiannoutsos, Constantin

PY - 1999

Y1 - 1999

N2 - Bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models, specifying a prior distribution on the model space and computations. We address these three issues for the logistic regression model. For the first, we propose an informative prior distribution for variable selection. Several theoretical and computational properties of the prior are derived and illustrated with several examples. For the second, we propose a method for specifying an informative prior on the model space, and for the third we propose novel methods for computing the marginal distribution of the data. The new computational algorithms only require Gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models. Several properties of the algorithms are also derived. The prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction y0 for the response vector and a quantity a0 quantifying the uncertainty in y0. Then, y0 and a0 are used to specify a prior for the regression coefficients semi-automatically. Examples using real data are given to demonstrate the methodology.

AB - Bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models, specifying a prior distribution on the model space and computations. We address these three issues for the logistic regression model. For the first, we propose an informative prior distribution for variable selection. Several theoretical and computational properties of the prior are derived and illustrated with several examples. For the second, we propose a method for specifying an informative prior on the model space, and for the third we propose novel methods for computing the marginal distribution of the data. The new computational algorithms only require Gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models. Several properties of the algorithms are also derived. The prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction y0 for the response vector and a quantity a0 quantifying the uncertainty in y0. Then, y0 and a0 are used to specify a prior for the regression coefficients semi-automatically. Examples using real data are given to demonstrate the methodology.

KW - Gibbs sampling

KW - Logistic regression

KW - Normal prior

KW - Posterior distribution

KW - Prior distribution

KW - Selection of variables

UR - http://www.scopus.com/inward/record.url?scp=0033474268&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033474268&partnerID=8YFLogxK

M3 - Article

VL - 61

SP - 223

EP - 242

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

SN - 1369-7412

IS - 1

ER -