Bayesian CART: Prior specification and posterior simulation

Journal of Computational and Graphical Statistics

Volumn 16, Issue 1, 2007, Pages 44-66

  Wu, Yuhong ^a   Tjelmeland, Håkon ^b   West, Mike ^a  

^a DUKE UNIVERSITY   (United States)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Pinball prior; Restructure moves; Tree prior specification

Indexed keywords

EID: 34147212595     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186007X180426     Document Type: Article

References (17)

1. Breiman, L., Friedman, J., Olshen, R., and Stone, C. (1984), Classification and Regression Trees, Belmont CA: Wadsworth.
2. Brooks, S. P., and Roberts, C. P. (1998), "Convergence Assessment Techniques for Markov Chain Monte Carlo," Statistics and Computing, 8, 319-335.
3. Chipman, H., George, E., and McCulloch, R. (1998), "Bayesian CART Model Search" (with discussion), Journal of the American Statistical Association, 93, 935-960.
4. _ (2000), "Hierarchical Priors for Bayesian CART Shrinkage," Statistics and Computing, 10, 17-24.
5. Clark, L., and Pregibon, D. (1992), "Tree-Based Models," in Statistical Models in S, eds. J. Chambers and T. Hastie, Pacific Grove, CA: Wadsworth.
6. Conover, W. (1971), Practical Nonparametric Statistics, New York: Wiley.
7. Cowles, M. K., and Carlin, B. P. (1996), "Markov Chain Monte-Carlo Convergence Diagnostics: A Comparative Review," Journal of the American Statistical Association, 91, 883-904.
8. Denison, D., Mallick, B., and Smith, A. (1998), "A Bayesian CART Algorithm," Biometrika, 85, 363-377.
9. Green, P. J. (1995), "Reversible Jump MCMC Computation and Bayesian Model Determination," Biometrika, 82, 711-732.
10. Huang, E., Chen, S., Dressman, H., Pittman, J., Tsou, M., Horng, C., Bild, A., Iversen, E., Liao, M., Chen, C., West, M., Nevins, J., and Huang, A. (2003), "Gene Expression Predictors of Breast Cancer Outcomes," The Lancet, 361, 1590-1596.
11. Liu, J. S., Liang, F. M., and Wong, W. H. (2000), "The Multiple-Try Method and Local Optimization in Metropolis Sampling," Journal of the American Statistical Association, 95, 121-134.
12. Pittman, J., Huang, E., Dressman, H., Horng, C., Cheng, S., Tsou, M., Chen, C., Bild, A., Iversen, E., Huang, A., Nevins, J., and West, M. (2004a), "Integrated Modeling of Clinical and Gene Expression Information for Personalized Prediction of Disease Outcomes," Proceedings of the National Academy of Sciences, 101, 8431-8436.
13. Pittman, J., Huang, E., Nevins, J., and West, M. (2003), "Prediction Tree Models in Clinico-Genomics," Bulletin of the International Statistical Institute, 54, 76.
14. Pittman, J., Huang, E., Wang, Q., Nevins, J., and West, M. (2004b), "Binary Analysis of Binary Prediction Tree Models for Retrospectively Sampled Outcomes," Biostatistics, 5, 587-601.
15. Qin, Z. S., and Liu, J. S. (2001), "Multi-point Metropolis Method with Application to Hybrid Monte Carlo," Journal of Computational Physics, 172, 827-840.
16. Tjelmeland, H. (2004), "Using all Metropolis-Hastings Proposals to Estimate Mean Values," Technical report, Statistics no. 4, Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway.
17. Wolberg, W., and Mangasarian, O. (1990), "Multisurface Method of Pattern Separation for Medical Diagnosis Applied to Breast Cytology," Proceedings of the National Academy of Sciences, 87, 9193-9196.