Predictive variable selection for the multivariate linear model.

We develop a predictive Bayesian approach to variable selection in the multivariate linear model. A criterion derived from the Bayesian predictive density is proposed and a calibration is provided for it. Reference and informative priors are discussed, and an automated method that focuses on the response variable is proposed for specifying informative priors for the regression parameters. Relationships between the proposed criterion and other several well-known criteria are examined. Illustrative examples involving real data are given to demonstrate the methodology.

[1]  Joseph G. Ibrahim,et al.  Predictive specification of prior model probabilities in variable selection , 1996 .

[2]  M. García-Closas,et al.  Asbestos-related diseases in construction carpenters. , 1995, American journal of industrial medicine.

[3]  Purushottam W. Laud,et al.  Predictive Model Selection , 1995 .

[4]  D. Schwartz,et al.  Longitudinal changes in lung function among asbestos-exposed workers. , 1994, American journal of respiratory and critical care medicine.

[5]  Purushottam W. Laud,et al.  A Predictive Approach to the Analysis of Designed Experiments , 1994 .

[6]  Chih-Ling Tsai,et al.  MODEL SELECTION FOR MULTIVARIATE REGRESSION IN SMALL SAMPLES , 1994 .

[7]  Adrian F. M. Smith,et al.  Bayesian Analysis of Linear and Non‐Linear Population Models by Using the Gibbs Sampler , 1994 .

[8]  Tom Leonard,et al.  Bayesian Inference for a Covariance Matrix , 1992 .

[9]  F. Graybill,et al.  Matrices with Applications in Statistics. , 1984 .

[10]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[11]  R. Mckay.  Variable Selection in Multivariate Regression: An Application of Simultaneous Test Procedures , 1977 .

[12]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[13]  J. Morris,et al.  Spirometric standards for healthy nonsmoking adults. , 2015, The American review of respiratory disease.

[14]  K. Gabriel,et al.  Simultaneous test procedures in multivariate analysis of variance , 1968 .

[15]  James M. Dickey,et al.  Matricvariate Generalizations of the Multivariate $t$ Distribution and the Inverted Multivariate $t$ Distribution , 1967 .

[16]  S. Geisser.  BAYESIAN ESTIMATION IN MULTIVARIATE ANALYSIS , 1965 .

[17]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .