Bayesian classification of tumours by using gene expression data

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

Volumn 67, Issue 2, 2005, Pages 219-234

  Mallick, Bani K ^a   Ghosh, Debashis ^b   Ghosh, Malay ^c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF FLORIDA   (United States)

Author keywords

Gibbs sampling; Markov chain Monte Carlo methods; Metropolis Hastings algorithm; Microarrays; Reproducing kernel Hubert space; Shrinkage parameters; Support vector machines

Indexed keywords

EID: 16244388597     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00498.x     Document Type: Article

References (45)

1. Albert, J. and Chib, S. (1993) Bayesian analysis of binary and polychotomous response data. J. Am. Statist. Ass., 88, 669-679.
2. Alon, U., Barkai, N., Notterman, D. A., Gish, K., Ybarra, S., Mack, D. and Levine, A. J. (1999) Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natn. Acad. Sci. USA, 96, 6745-6750.
3. Aronszajn, N. (1950) Theory of reproducing kernels. Trans. Am. Math. Soc., 68, 337-404.
4. Bernardo, J. M. (1979) Expected information as expected utility. Ann. Statist., 7, 686-690.
5. Bishop, C. and Tipping, M. (2000) Variational relevance vector machines. In Proc. 16th Conf. Uncertainty and Artificial Intelligence (eds C. Boutilier and M. Goldszmidt), pp. 46-53. San Francisco: Morgan Kauffman.
6. Brown, M. P. S., Grundy, W. N., Lin, D., Cristianini, N., Sugnet, C. W., Furey, T. S. and Haussler, D. (2000) Knowledge-based analysis of microarray gene expression data by using support vector machines. Proc. Natn. Acad. Sci. USA, 97, 262-267.
7. Cristianini, N. and Shawe-Taylor, J. (2000) An Introduction to Support Vector Machines. Cambridge: Cambridge University Press.
8. Denison, D., Holmes, C., Mallick, B. and Smith, A. F. M. (2002) Bayesian Methods for Nonlinear Classification and Regression. London: Wiley.
9. DeRisi, J. L., Iyer, V. R. and Brown, P. O. (1997) Exploring the metabolic and genetic control of gene expression on a genomic scale. Science, 278, 680-685.
10. Dudoit, S., Fridlyand, J. and Speed, T. P. (2002) Comparison of discrimination methods for the classification of tumors using gene expression data. J. Am. Statist. Ass., 97, 77-87.
11. Figueiredo, M. (2002) Adaptive sparseness using Jeffreys prior. In Neural Information Processing Systems 14 (eds T. Dietterich, S. Becker and Z. Ghahramani), pp. 697-704. Cambridge: MIT Press.
12. Fix, E. and Hodges, J. L. (1951) Discriminatory analysis-nonparametric discrimination: consistency properties. US Air Force School of Aviation Medicine, Randolf Field.
13. Gelfand, A. ( 1996) Model determination using sampling-based methods. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter), pp. 145-158. London: Chapman and Hall.
14. Gelfand, A. and Smith, A. F. M. (1990) Sampling-based approaches to calculating marginal densities. J. Am. Statist. Ass., 85, 398-409.
15. Gelman, A. (1996) Inference and monitoring convergence. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter), pp. 131-140. London: Chapman and Hall.
16. Golub, T. R., Slonim, D., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J., Coller, H., Loh, M., Downing, J., Caligiuri, M., Bloomfield, C. and Lander, E. (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science, 286, 531-537.
17. Hastie, T. J. and Tibshirani, R. J. (1990) Generalized Additive Models. London: Chapman and Hall.
18. Hedenfalk, I., Duggan, D., Chen, Y., Radmacher, M., Bittner, M., Simon, R., Meltzer, P., Gusterson, B., Esteller, M., Kallioniemi, O. P., Wilfond, B., Borg, A. and Trent, J. (2001) Gene expression profiles in hereditary breast cancer. New Engl. J. Med., 344, 539-548.
19. Herbrich, R. (2002) Learning Kernel Classifiers. Cambridge: MIT Press.
20. Holmes, C. and Held, L. (2003) Bayesian auxiliary variable models for binary and polychotomous regression. Technical Report. Imperial College, London.
21. Kimeldorf, G. and Wahba, G. (1971) Some results on Tchebycheffian spline functions. J. Math. Anal. Applic., 33, 82-95.
22. Lee, K. E., Sha, N., Dougherty, E., Vannucci, M. and Mallick, B. (2003) Gene selection: a Bayesian variable selection approach. Bioinformatics, 19, 90-97.
23. MacKay, D. (1996) Bayesian non-linear modelling for the 1993 energy prediction competition. In Maximum Entropy and Bayesian Methods (ed. G. Heidbreder), pp. 221-234. Dordrecht: Kluwer.
24. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. and Teller, E. (1953) Equation of state calculations by fast computing machines. J. Chem. Phys., 21, 1087-1092.
25. Moler, E. J., Chow, M. L. and Mian, I. S. (2000) Analysis of molecular profile data using generative and discriminative methods. Physiol. Genet., 4, 109-126.
26. Neal, R. (1996) Bayesian Learning for Neural Networks. New York: Springer.
27. Parzen, E. (1970) Statistical inference on time series by rkhs methods. In Proc. 12th Bienn. Sem. (ed. R. Pyke), pp. 1-37. Montreal: Canadian Mathematical Congress.
28. Pontil, M., Evgeniou, T. and Poggio, T. (2000) Regularization networks and support vector machines. Adv. Cornput. Math., 13, 1-50.
29. Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge: Cambridge University Press.
30. Rosenblatt F. (1962) Principles of Neurodynamics. New York: Spartan.
31. Roth, V. (2002) The generalized LASSO: a wrapper approach to gene selection for microarray data. Department of Computer Science, University of Bonn, Bonn.
32. Schena, M., Shalon, D., Davis, R. and Brown, P. (1995) Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science, 270, 467-470.
33. Schölkopf, B. and Smola, A. (2002) Learning with Kernels. Cambridge: MIT Press.
34. Sollich, P. (2001) Bayesian methods for support vector machines: evidence and predictive class probabilities. Mach. Learn., 46, 21-52.
35. Specht, D. F. (1990) Probabilistic neural networks. New. Netwrks, 3, 109-118.
36. Tipping, M. (2000) The relevance vector machine. In Neural Information Processing Systems 12 (eds S. Solla, T. Leen and K. Muller), pp. 652-658. Cambridge: MIT Press.
37. Tipping, M. (2001) Sparse Bayesian learning and the relevance vector machine. J. Mach. Learn. Res., 1, 211-244.
38. Vapnik, V. N. (2000) The Nature of Statistical Learning Theory, 2nd edn. New York: Springer.
39. Wahba, G. (1990) Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.
40. Wahba, G. (1999) Support vector machines, reproducing kernel hilbert spaces and the randomized GACV. In Advances in Kernel Methods (eds B. Schölkopf, C. Surges and A. Smola), pp. 69-88. Cambridge: MIT Press.
41. Wahba, G., Lin, Y., Lee, Y. and Zhang, H. (2002) Optimal properties and adaptive tuning of standard and nonstandard support vector machines. In Nonlinear Estimation and Classification (eds D. Denison, M. Hansen, C. Holmes, B. Mallick and B. Yu), pp. 125-143. New York: Springer.
42. West, M. (2003) Bayesian factor regression models in the "large p, small n" paradigm. In Bayesian Statistics 7 (eds J. M. Bernardo, M. Bayarri, A. P. Dawid, J. Berger, D. Heckerman, A. F. M. Smith and M. West), pp. 723-732. Oxford: Oxford University Press.
43. Williams, C. and Barber, D. (1998) Bayesian classification with Gaussian priors. IEEE Trans. Pattn Anal. Mach. Intell., 20, 1342-1351.
44. Xiong, M., Jin, L., Li, W. and Boerwinkle, E. (2000) Computational methods for gene expression-based tumor classification. Biotechniques, 29, 1264-1270.
45. Zhu, J. and Hastie, T. (2002) Kernel logistic regression and the import vector machine. In Neural Information Processing Systems 14 (eds T. Dietterich, S. flecker and Z. Ghahramani), pp. 1081-1088. Cambridge: MIT Press.