Bayesian wavelet-based curve classification via discriminant analysis with Markov random tree priors

Statistica Sinica

Volumn 22, Issue 2, 2012, Pages 465-488

  Stingo, Francesco C ^a   Vannucci, Marina ^b   Downey, Gerard ^c  

^a UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

^b Rice University   (United States)

^c TEAGASC FOOD RESEARCH CENTRE   (Ireland)

Author keywords

Bayesian variable selection; Classification and pattern recognition; Markov chain Monte Carlo; Markov random tree prior; Wavelet based modeling

Indexed keywords

EID: 84858382394     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: 10.5705/ss.2010.141     Document Type: Article

References (33)

1. Antoniadis, A., Bigot, J. and Sapatinas, T. (2001). Wavelet estimators in nonparametric regression: A comparative simulation study. J. Statist. Software 6, 1-83. (Pubitemid 39217771)
2. Brown, P. (1993). Measurement, Regression, and Calibration. Oxford University Press.
3. Brown, P., Fearn, T. and Vannucci, M. (2001). Bayesian wavelet regression on curves with application to a spectroscopic calibration problem. J. Amer. Statist. Assoc. 96, 398-408.
4. Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Conference Series.
5. Dawid, A. P. (1981). Some matrix-variate distribution theory: notational considerations and a bayesian application. Biometrika 68, 265-274.
6. Dean, N., Murphy, T. and Downey, G. (2006). Using unlabelled data to update classification rules with applications in food authenticity studies. J. Roy. Statist. Soc. Ser. C 55, 1-14. (Pubitemid 43424076)
7. Dobra, A., Jones, B., Hans, C., Nevins, J. and West, M. (2004). Sparse graphical models for exploring gene expression data. J. Multivariate Anal. 90, 196-212. (Pubitemid 41137013)
8. Donoho, D. and Johnstone, I. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-455.
9. Downey, G. (1996). Authentication of food and food ingredients by near infrared spectroscopy. J. Near Infrared Spectroscopy 4, 47-61. (Pubitemid 126510347)
10. Fearn, T., Brown, P. and Besbeas, P. (2002). A Bayesian decision theory approach to variable selection for discrimination. Statist. Comput. 12, 253-260. (Pubitemid 37132818)
11. George, E. I. and McCulloch, R. E. (1993). Variable selection via Gibbs sampling. J. Amer. Statist. Assoc. 88, 881-889.
12. George, E. I. and McCulloch, R. E. (1997). Approaches for Bayesian variable selection. Statist. Sinica 7, 339-373. (Pubitemid 127473668)
13. Gonzalez, R. and Woods, R. (2002). Digital Image Processing. Prentice Hall.
14. He, L. and Carin, L. (2009). Exploiting structure in wavelet-based Bayesian compressive sensing. IEEE Trans. Signal Process. 57, 3488-3497.
15. Jolliffe, I. (1986). Principal Component Analysis. Springer-Verlag.
16. Kass, R. and Wasserman, L. (1996). The selection of prior distributions by formal rules. J. Amer. Statist. Assoc. 91, 1343-70.
17. Kim, S., Tadesse, M. and Vannucci, M. (2006). Variable selection in clustering via Dirichlet process mixture models. Biometika 93, 877-893. (Pubitemid 44973874)
18. Li, F. and Zhang, N. (2010). Bayesian variable selection in structured high-dimensional covariate space with application in Genomics. J. Amer. Statist. Assoc. 105, 1202-14.
19. Madigan, D. and York, J. (1995). Bayesian graphical models for discrete data. Internat. Statist. Rev. 63, 215-232.
20. Mallat, S. (1989). Multiresolution approximations and wavelet orthonormal bases of l2(IR)'. Trans. Amer. Math. Soc. 315, 69-87.
21. Morris, J. and Carroll, R. (2006). Wavelet-based functional mixed models. J. Roy. Statist. Soc. Ser. B 68, 179-199. (Pubitemid 43344992)
22. Murphy, T., Dean, N. and Raftery, A. (2010). Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications. Ann. Appl. Statist. 4, 396-421.
23. Newton, M., Noueiry, A., Sarkar, D. and Ahlquist, P. (2004). Detecting differential gene expression with a semiparametric hierarchical mixture method. Biostatistics 5, 155-176. (Pubitemid 41180221)
24. Oliveri, P., Di Egidio, V., Woodcock, T. and Downey, G. (2011). Application of class-modelling techniques to near infrared data for food authentication purposes. Food Chemistry 125, 1450-1456.
25. Propp, J. and Wilson, D. (1996). Exact sampling with coupled markov chains and applications to statistical mechanics. Random Structures Algorithms 9, 223-252.
26. Ray, S. and Mallick, B. (2006). Functional clustering by Bayesian wavelet methods. J. Roy. Statist. Soc. Ser. B 68, 305-332. (Pubitemid 43344998)
27. Richardson, S. and Green, P. (1997). On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. Roy. Statist. Soc. Ser. B 59, 731-92. (Pubitemid 127686979)
28. Sha, N., Vannucci, M., Tadesse, M. G., Brown, P. J., Dragoni, I., Davies, N., Roberts, T. C., Contestabile, A., Salmon, N., Buckley, C. and Falciani, F. (2004). Bayesian variable selection in multinomial probit models to identify molecular signatures of disease stage. Biometrics 60, 812-19. (Pubitemid 39181128)
29. Shapiro, J. (1993). Embedded image coding using Zeotrees of Wavelet coefficients. IEEE Trans. Signal Process. 41, 3445-3462.
30. Tadesse, M., Sha, N. and Vannucci, M. (2005). Bayesian variable selection in clustering highdimensional data. J. Amer. Statist. Assoc. 100, 602-617. (Pubitemid 40816597)
31. Vannucci, M. and Corradi, F. (1999). Covariance structure of wavelet coefficients: Theory and models in a Bayesian perspective. J. Roy. Statist. Soc. Ser. B 61, 971-986.
32. Vidakovic, B. (1999). Statistical Modeling by Wavelets. Wiley.
33. Wasserman, L. (2000). Asymptotic inference for mixture models using data-dependent priors. J. Roy. Statist. Soc. Ser. B 62, 159-80.