Functional clustering by Bayesian wavelet methods

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

Volumn 68, Issue 2, 2006, Pages 305-332

  Ray, Shubhankar ^a   Mallick, Bani ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Functional clustering; Mixture of Dirichlet processes; Nonparametric Bayesian model; Wavelets

Indexed keywords

EID: 33644782021     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2006.00545.x     Document Type: Article

References (33)

1. Abramovicli, F., Sapatinas, T. and Silverman, B. W. (1998) Wavelet thresholding via a Bayesian approach. J. R. Statist. Soc. B, 60, 725-749.
2. Antoniak, C. E. (1974) Mixtures of Dirichlet processes with applications to nonparametric problems. Ann. Statist., 2, 1152-1174.
3. Banerjee, S. (2004) On geodetic distance computations in spatial modelling. Biometrics, 61, 617-625.
4. Banfield, J. D. and Raftery, A. E. (1993) Model-based Gaussian and non-Gaussian clustering. Biometrics, 49, 803-821.
5. Basu, S. and Chib, S. (2003) Marginal likelihood and Bayes factors for Dirichlet process mixture models. J. Am. Statist. Ass., 98, 224-235.
6. Blackwell, D. and MacQueen, J. B. (1973) Ferguson distributions via Polya urn schemes. Ann. Statist., 1, 353-355.
7. Bush, C. S. and MacEachern, S. N. (1996) A semi-parametric Bayesian model for randomized block designs. Biometrika, 83, 221-227.
8. Chaloner, K. and Brant, R. (1988) A Bayesian approach to outlier detection and residual analysis. Biometrika, 75, 651-660.
9. Clyde, M. and George, E. I. (2000) Flexible empirical Bayes estimation for wavelets. J. R. Statist. Soc. B, 62, 681-698.
10. Clyde, M., Parmigiani, G. and Vidakovic, B. (1998) Multiple shrinkage and subset selection in wavelets. Biometrika, 85, 391-402.
11. Daubechies, I. (1992) Ten Lectures in Wavelets. Philadelphia: Society for Industrial and Applied Mathematics.
12. De Canditiis, D. and Vidakovic, B. (2004) Wavelet Bayesian block shrinkage via mixtures of normal inverse gamma priors. J. Comput. Graph. Statist., 13, 383-398.
13. Donoho, D. L. and Johnstone, I. M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455.
14. Donoho, D. L. and Johnstone, I. M. (1995) Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Ass., 90, 1200-1224.
15. Escobar, M. D. and West, M. (1995) Bayesian density estimation and inference using mixtures. J. Am. Statist. Ass., 90, 577-588.
16. Ferguson, T. S. (1973) A Bayesian analysis of some nonparametric problems. Ann. Statist., 1, 209-230.
17. Gelfand, A. E., Kim, H. K., Sirmans, C. F. and Banerjee, S. (2003) Spatial modelling with spatially varying coefficient processes. J. Am. Statist. Ass., 98, 387-396.
18. Green, P. J. (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.
19. James, G. and Sugar, C. (2003) Clustering for sparsely sampled functional data. J. Am. Statist. Ass., 1, 98, 397-408.
20. Klevecz, R. R. (2000) Dynamic architecture of the yeast cell cycle uncovered by wavelet decomposition of expression array data. FunctnlIntegr. Genom., 1, 186-192.
21. Korwar, R. M. and Hollander, M. (1973) Contributions to the theory of Dirichlet Processes. Ann. Probab., 1, 705-711.
22. Kovac, A. and Silverman, B. W. (2000) Extending the scope of wavelet regression methods by coefficient-dependent thresholding. J. Am. Statist. Ass., 95, 172-183.
23. Medvedovic, M. and Sivaganesan, S. (2002) Bayesian infinite mixture model-based clustering of gene expression profiles. Bioinformatics, 18, 1194-1206.
24. Petisky, M. and Vidakovic, B. (2001) On non-equally spaced wavelet regression. Ann. Inst. Statist. Math., 53, 681-690.
25. Quintana, F. A. and Iglesias, P. L. (2003) Bayesian clustering and product partition models. J. R. Statist. Soc. B, 65, 557-574.
26. Ren, B., Robert, F., Wyrick, J. J., Aparicio, O., Jennings, E. J., Simon, J., Zeitlinger, J., Schreiber, J., Hannett, N., Kanin, E., Volkert, T. L., Wilson, C. J., Bell, S. P. and Young, R. A. (2000) Genome-wide location and function of DNA binding proteins. Science, 290, 2306-2309.
27. Rivoirard, J. (1994) Introduction to Disjunctive Kriging and Non-linear Geostatistics. Oxford: Clarendon.
28. Spellman, P. T., Sherlock, G., Zhang, M. Q., Iyer, V. R., Anders, K., Eisen, M. B., Brown, P. O., Botstein, D. and Futcher, B. (1998) Comprehensive identification of cell cycle-regulated genes of the Yeast Saccharomyces cerevisiae by microarray hybridization. Molec. Biol. Cell, 9, 3273-3297.
29. Sweldens, W. (1996) The lifting scheme: a custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal., 3, 186-200.
30. Vidakovic, B. (1998) Nonlinear wavelet shrinkage with Bayes rule and Bayes factors. J. Am. Statist. Ass., 93, 173-179.
31. Wakefield, J., Zhou, C. and Self, S. (2003) Modelling gene expression over time: curve clustering with informative prior distributions. In Bayesian Statistics 7 (eds J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West). Oxford: Oxford University Press.
32. Widmann, M. and Bretherton, C. S. (2000) Validation of mesoscale precipitation in the NCEP reanalysis using a new grid-cell data set for the northwestern United States. J. Clim., 13, 1936-1950.
33. Yeung, K., Fraley, C., Raftery, A. and Ruzzo, W. (2001) Model-based clustering and data transformations for gene expression data. Bioinformatics, 17, 977-987.