The choice of variables in multivariate regression: A non-conjugate Bayesian decision theory approach

Biometrika

Volumn 86, Issue 3, 1999, Pages 635-648

  Brown, Philip J ^a   Fearn, Tom ^b   Vannucci, Marina ^c  

^a UNIVERSITY OF KENT   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

^c TEXAS A AND M UNIVERSITY   (United States)

Author keywords

.utility; Bayesian decision theory; Determinism; Multivariate regression; Near infrared spectroscopy; Non conjugate distribution; Prediction; Quadratic loss; Simulated annealing

Indexed keywords

EID: 0000294132     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/86.3.635     Document Type: Article

References (22)

1. BERNARDO, J. M. & SMITH, A. F. M. (1994). Bayesian Theory. Chichester: Wiley.
2. BROOKS, R. J. (1974). On the choice of an experiment for prediction in linear regression. Biometrika 61,303-11.
3. BROWN, P. J. (1993). Measurement, Regression, and Calibration. Oxford: Clarendon.
4. BROWN, P. J., LE, N. D. & ZIDEK, J. V. (1994). Inference for a covariance matrix. In Aspects of Uncertainty: A Tribute to D. V. Lindley Ed. P. R. Freeman and A. F. M. Smith, pp.77-92. Chichester: Wiley.
5. BROWN, P. J. & MäKELäINEN, T. (1992). Regression, sequenced measurements and coherent calibration. In Bayesian Statistics 4 Ed. J. M. Bernardo, J. Berger, A. P. Dawid and A. F. M. Smith, pp. 97-108. Oxford: Clarendon.
6. BROWN, P. J., VANNUCCI, M. & FEARN, T. (1998a). Bayesian wavelength selection in multi-component analysis. J. Chemomet. 12, 173-82.
7. BROWN, P. J., VANNUCCI, M. & FEARN, T. (1998b). Multivariate Bayesian variable selection and prediction. J. R. Statist. Soc. B 60, 627-41.
8. CLYDE, M., DESIMONE, H. & PARMIGIANI, G. (1996). Prediction via orthogonalised model mixing. J. Am. Statist. Assoc. 91, 1197-208.
9. DAWID, A. P. (1981). Some matrix-variable distribution theory: Notational considerations and a Bayesian application. Biometrika 68, 265-74.
10. DAWID, A. P. (1988). The infinite regress and its conjugate analysis. In Bayesian Statistics 3 Ed. J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, pp. 95-110. Oxford: Clarendon.
11. FANG, B. Q. & DAWID, A. P. (2000). Nonconjugate Bayesian regression on many variables. J. Statist. Plan. Infer. To appear.
12. GEORGE, E. I. & McCuLLOCii, R. E. (1997). Approaches for Bayesian variable selection. Statist. Sinica 7, 339-73.
13. GOLUB, G. H., HEATH, M. & WAHBA, G. (1979). Generalised cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215-23.
14. LEMPERS, F. B. (1971). Posterior Probabilities of Alternative Models. Rotterdam: Rotterdam University Press.
15. LINDLEY, D. V. (1968). The choice of variables in multiple regression (with Discussion). J. R. Statist. Soc. B 30, 31-66.
16. MäKELäINEN, T. & BROWN, P. J. (1988). Coherent priors for ordered regressions. In Bayesian Statistics 3 Ed. J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, pp. 677-96. Oxford: Clarendon.
17. MITCHELL, T. J. & BEAUCHAMP, J. J. (1988). Bayesian variable selection in linear regression. J. Am. Statist. Assoc. 83, 1023-36.
18. MOUCHART, M. & SIMAR, L. (1980). Least squares approximation in Bayesian analysis. In Bayesian Statistics 1 Ed. J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, pp. 207-22. Valencia University Press.
19. OSBORNE, B. G., FEARN, T., MILLER, A. R. & DOUGLAS, S. (1984). Application of near infrared reflectance spectroscopy to compositional analysis of biscuits and biscuit doughs. J. Sci. Food Agric. 35, 99-105.
20. PRESS, S. J. (1982). Applied Multivariate Analysis: Using Bayesian and Freqitentist Methods of Inference, 2nd ed. Malabar, FL: Krieger.
21. RAFTERY, A. E., MADIGAN, D. & HOETING, J. A. (1997). Bayesian model averaging for linear regression models. J. Am. Statist. Assoc. 92, 179-91.
22. SEBER, G. A. F. (1984). Multivariate Observations. New York: Wiley.