Predictive bayesian model selection

American Journal of Mathematical and Management Sciences

Volumn 31, Issue 1-2, 2011, Pages 13-38

  Ando, Tomohiro ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Effective number of parameters; Empirical Bayes Markov chain Monte Carlo; Hierarchical Bayesian model; Model misspecification

Indexed keywords

BAYESIAN MODEL; BAYESIAN MODEL SELECTION; EFFECTIVE NUMBER OF PARAMETERS; HIERARCHICAL BAYESIAN MODELS; INFORMATION CRITERION; MARKOV CHAIN MONTE CARLO; MISSPECIFICATION; MONTE CARLO SIMULATION; POSTERIOR MEANS; PREDICTIVE DISTRIBUTIONS; STUDY AREAS;

MONTE CARLO METHODS;

BAYESIAN NETWORKS;

EID: 84868296532     PISSN: 01966324     EISSN: None     Source Type: Journal    
DOI: 10.1080/01966324.2011.10737798     Document Type: Article

References (37)

1. Aitkin, M. (1991). Posterior Bayes factors (with discussion). Journal of the Royal Statistical Society, B53, 111-128.
2. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control. AC-19, 716-723.
3. Akaike, H. (1991). Discussion on ‘Posterior Bayes factors”. Journal of the Royal Statistical Society B53, 135.
4. Ando, T. (2007). Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models. Biometrika. 94, 443-458.
5. Ando, T. (2010a). Bayesian statistical modeling and model selection. Chap-man&Hall/CRC, London.
6. Ando, T. (2010b). Bayesian portfolio selection under a multifactor asset return model with predictive Bayesian model selection. Proceeding of International Association for the Scientific Knowledge Global Management 2010, 111-120.
7. Ando, T. and Tsay, R. (2010). Predictive marginal likelihood for the Bayesian model selection and averaging. International Journal of Forecasting, 26, 744-763.
8. Ando, T., Konishi, S. and Imoto, S. (2008). Nonlinear regression modeling via regularized radial basis function networks. Journal of Statistical Planning and Inference. 138, 3616-3633.
9. Barndorff-Nielsen, O. E. and Cox, D. R. (1989). Asymptotic Techniques for Use in Statistics. Chapman and Hall, London.
10. Berg, A., Meyer, R. and Yu, J. (2004). Deviance information criterion comparing stochastic volatility models. Journal of Business and Economic Statistics. 22, 107-120.
11. Berger, J. O. and Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of The American Statistical Association. 91, 109-122.
12. Celeux, G., Forbes, F., Robert, C. and Titterington, D. M. (2006). Deviance information criteria for missing data models, Bayesian Analysis, 1, 651-674.
13. Chib, S. (1995). Marginal Likelihood from the Gibbs Output. .Journal of the American Statistical Association. 90. 1313-1321.
14. Chib, S., Nardari, F. and Shephard, N. (2002). Markov Chain Monte Carlo Methods for Stochastic Volatility Models. Journal of Econometrics. 108, 281-316.
15. Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
16. Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties (with Discussion). Statistical Science. 11, 89-121.
17. Gelfand, A. E. and Dev, D. K. (1994). Bayesian model choice: asymptotic and exact calculations. Journal of the Royal Statistical Society, B56, 501-514.
18. Gelfand, A. and Ghosh, S. (1998). Model choice: a minimum posterior predictive loss approach. Biometrika. 85, 1-11.
19. Hurvich, C. M., Simonoff, J. S. and Tsai, C.-L. (1998), Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society, B60, 271-293.
20. Kadane, J. B. and Lazar, N. A. (2004). Methods and criteria for model selection. Journal of the American Statistical Association. 99, 279-290.
21. Kass, R. and Raftery, A. (1995). Bayes factors and model uncertainty. Journal of the American Statistical Association. 90, 773-795.
22. Kim, S., Shephard, N. and Chib, S. (1998). Stochastic volatility: likelihood inference comparison with ARCH models. Review of Economic Studies. 65, 361-393.
23. Konishi, S. and Kitagawa, G. (1996). Generalized information criteria in model selection. Biometrika. 83, 875-890.
24. Konishi, S., Ando, T. and Imoto, S. (2004). Bayesian information criteria and smoothing parameter selection in radial basis function networks. Biometrika. 91, 27-43.
25. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models. Chapman and Hall, London.
26. Mukhopadhyaya, N., Ghosh, J. K. and Berger, J. O. (2003). Some Bayesian predictive approaches to model selection. Statistics and Probability Letters, 73, 369-379.
27. Murata, N., Yoshizawa, S. and Amari, S. (1994). Network information criterion determining the number of hidden units for an artificial neural network model. IEEE Transactions on Neural Networks. 5, 865-872.
28. Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap (with Discussion). Journal of the Royal Statistical Society, B56, 3-48.
29. O’Hagan, A. (1995). Fractional Bayes factors for model comparison (with Discussion). Journal of the Royal Statistical Society, B57, 99-138.
30. Perez, J. M. and Berger, J. O. (2002). Expected-posterior prior distributions for model selection. Biometrika. 89, 491-512.
31. Plummer, M. (2008). Penalized loss functions for Bayesian model comparison. Biostatistics. 9, 523-539.
32. Rahul Pandev, G. S. and Singh, O. P. (2009). Population Projection of Kerala using Bayesian Methodology. Asian Journal of Applied Sciences, 2, 402-413.
33. Robert, C. P. and Titterington D. M. (2002). Discussion on Bayesian measures of model complexity and fit’. Journal of the Royal Statistical Society, B64, 621-622.
34. Singh, O. P., Pandey G. S. and Rahul R (2007). Population projection of India (2001-2051) using MCMC technique in Bayesian inference. American Journal of Mathematical and Management Sciences, 27, 139-152.
35. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. & van der Linde, A. (2002). Bayesian measures of model complexity and fit (with Discussion). Journal of the Royal Statistical Society, B64, 583-639.
36. van der Linde, A. (2005). DIC in variable selection. Statistica Neerlandica. 59, 45-56.
37. Zellner, A. and Ando T. (2010). A Direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model with informative prior (in Japanese). Journal of the Japan Statistical Society, 39, 297-312.