Functional regression via variational bayes

Electronic Journal of Statistics

Volumn 5, Issue , 2011, Pages 572-602

  Goldsmith, Jeff ^a   Wand, Matt P ^b   Crainiceanu, Ciprian ^a  

^a JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

^b UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

Author keywords

Approximate bayesian inference; Markov chain monte carlo; Penalized splines

Indexed keywords

EID: 79960998417     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-EJS619     Document Type: Article

References (25)

1. Basser, P., Mattiello, J. and LeBihan, D. (1994). MR Diffusion Tensor Spectroscopy and Imaging. Biophysical Journal 66 259-267.
2. Basser, P., Pajevic, S., Pierpaoli, C. and Duda, J. (2000). In vivo fiber tractography using DT-MRI data. Magnetic Resonance in Medicine 44 625-632.
3. Bishop, C. M. (2006). Pattern Recognition and Machine Learning. New York: Springer. MR2247587
4. Cardot, H., Ferraty, F. and Sarda, P. (1999). Functional Linear Model. Statistics and Probability Letters 45 11-22. MR1718346
5. Crainiceanu, C. M. and Goldsmith, J. (2010). Bayesian Functional Data Analysis using WinBUGS. Journal of Statistical Software 32 1-33.
6. Goldsmith, J., Bobb, J., Crainiceanu, C. M., Caffo, B. and Reich, D. (To Appear). Penalized Functional Regression. Journal of Computational and Graphical Statistics.
7. Goldsmith, J., Crainiceanu, C. M., Caffo, B. and Reich, D. (2011). A Case Study of Longitudinal Association Between Disability and Neuronal Tract Measurements. Under Review.
8. Gronwall, D. M. A. (1977). Paced auditory serial-addition task: A mea- sure of recovery from concussion. Perceptual and Motor Skills 44 367-373.
9. James, G. M., J, W. and J, Z. (2009). Functional Linear Regression That's Interpretable. Annals of Statistics 37 2083-2108. MR2543686
10. Jordan, M. I. (2004). Graphical models. Statistical Science 19 140-155. MR2082153
11. Jordan, M. I., Ghahramani, Z., Jaakkola, T. S. and Saul, L. K. (1999). An Introduction to Variational Methods for Graphical Models. Machine Learning 37 183-233.
12. Kullback, S. and Leibler, D. (1951). On Information and Sufficiency. The Annals of Mathematical Statistics 22 79-86. MR0039968
13. Lang, S. and Brezger, A. (2004). Bayesian P-splines. Journal of Computational and Graphical Statistics 13 183-212. MR2044877
14. LeBihan, D., Mangin, J., Poupon, C. and Clark, C. (2001). Dif- fusion Tensor Imaging: Concepts and Applications. Journal of Magnetic Resonance Imaging 13 534-546.
15. Lin, X., Tench, C. R., Morgan, P. S. and Constantinescu, C. S. (2008). Use of combined conventional and quantitative MRI to quantify pathology related to cognitive impairment in multiple sclerosis. Journal of Neurology, Neurosurgery, and Psychiatry 237 437-441.
16. McGrory, C. A., Titterington, D. M., Reeves, R. and Pettitt, A. N. (2009). Variational Bayes for Estimating the Parameters of a Hidden Potts Model. Statistics and Computing 19 329-340. MR2516223
17. Mori, S. and Barker, P. (1999). Diffusion magnetic resonance imaging: its principle and applications. The Anatomical Record 257 102-109.
18. Müller, H.-G. and Stadtmüller, U. (2005). Generalized functional linear models. Annals of Statistics 33 774-805. MR2163159
19. Ormerod, J. and Wand, M. P. (2010). Explaining Variational Approximations. The American Statistician 64 140-153.
20. Ozturk, A., Smith, S., Gordon-Lipkin, E., Harrison, D., Shiee, N., Pham, D., Caffo, B., Calabresi, P. and Reich, D. (2010). MRI of the corpus callosum in multiple sclerosis: association with disability. Multiple Sclerosis 16 166-177.
21. Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis. New York: Springer. MR2168993
22. Reiss, P. and Ogden, R. (2007). Functional Principal Component Re- gression and Functional Partial Least Squares. Journal of the American Statistical Association 102 984-996. MR2411660
23. Ruppert, D.,Wand, M. P. and Carroll, R. J. (2003). Semiparametric Regression. Cambridge: Cambridge University Press. MR1998720
24. Teschendorff, A. E., Wang, Y., Barbosa-Morais, N. L., Bren- ton, J. D. and Caldas, C. (2005). A Variational Bayesian Mixture Modeling Framework for Cluster Analysis of Gene-Expression Data. Bioinformatics 21 3025-3033.
25. Titterington, D. M. (2004). BayesianMethods for Neural Networks and Related Models. Statistical Science 19 128-139. MR2082152