Fast Bayesian model assessment for nonparametric additive regression

Computational Statistics and Data Analysis

Volumn 71, Issue , 2014, Pages 347-358

  McKay Curtis, S ^a   Banerjee, Sayantan ^a   Ghosal, Subhashis ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Group LASSO; Laplace approximation; Model uncertainty; Penalized regression; Variable selection

Indexed keywords

GROUP LASSOS; LAPLACE APPROXIMATION; MODEL UNCERTAINTIES; PENALIZED REGRESSION; VARIABLE SELECTION;

LAPLACE TRANSFORMS; LINEAR REGRESSION; MARKOV PROCESSES; MATHEMATICAL MODELS; UNCERTAINTY ANALYSIS;

BAYESIAN NETWORKS;

EID: 84889084527     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2013.05.012     Document Type: Article

References (41)

1. H. Akaike A new look at the statistical model identification IEEE Trans. Automat. Control AC-19 1974 716 723 System Identification and Time-Series Analysis
2. M. Avalos, Y. Grandvalet, and C. Ambroise Regularization methods for additive models Advances in Intelligent Data Analysis V 2003 509 520
3. M.M. Barbieri, and J.O. Berger Optimal predictive model selection Ann. Statist. 32 2004 870 897 (Pubitemid 41250287)
4. D. Barry Nonparametric Bayesian regression Ann. Statist. 14 1986 934 953
5. C. Belitz, and S. Lang Simultaneous selection of variables and smoothing parameters in structured additive regression models Comput. Statist. Data Anal. 53 2008 61 81
6. H.D. Bondell, and B.J. Reich Simultaneous regression shrinkage, variable selection, and supervised clustering of predictors with OSCAR Biometrics 64 2008 115 123 (Pubitemid 351316873)
7. L. Breiman Better subset regression using the nonnegative garrote Technometrics 37 1995 373 384
8. A. Buja, T. Hastie, and R. Tibshirani Linear smoothers and additive models Ann. Statist. 17 1989 453 555
9. Z.H. Chen Fitting multivariate regression functions by interaction spline models J. R. Stat. Soc. Ser. B Stat. Methodol. 55 1993 473 491
10. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani Least angle regression Ann. Statist. 32 2004 407 499 (Pubitemid 41250302)
11. M.D. Ernst A multivariate generalized Laplace distribution Comput. Statist. 13 1998 227 232
12. J. Fan, and R. Li Variable selection via nonconcave penalized likelihood and its oracle properties J. Amer. Statist. Assoc. 96 2001 1348 1360 (Pubitemid 33695585)
13. J.H. Friedman Multivariate adaptive regression splines Ann. Statist. 19 1991 1 141
14. E.I. George The variable selection problem J. Amer. Statist. Assoc. 95 2000 1304 1308
15. E. George, and R. McCulloch Variable selection via Gibbs sampling J. Amer. Statist. Assoc. 88 1993 881 889
16. C. Gu Smoothing Spline ANOVA Models Springer Series in Statistics 2002 Springer-Verlag New York
17. P. Gustafson Bayesian regression modeling with interactions and smooth effects J. Amer. Statist. Assoc. 95 2000 795 806
18. T.J. Hastie, and R.J. Tibshirani Generalized Additive Models Monographs on Statistics and Applied Probability vol. 43 1990 Chapman and Hall Ltd. London
19. J. Huang, J.L. Horowitz, and F. Wei Variable selection in nonparametric additive models Ann. Statist. 38 2010 2282 2313
20. W.Y. Hwang, H.H. Zhang, and S. Ghosal FIRST: combining forward iterative selection and shrinkage in high dimensional sparse linear regression Stat. Interface 2 2009 341 348
21. J. Lafferty, and L. Wasserman Rodeo: sparse, greedy nonparametric regression Ann. Statist. 36 2008 28 63
22. B. Liebmann, A. Friedl, and K. Varmuza Determination of glucose and ethanol in bioethanol production by near infrared spectroscopy and chemometrics Anal. Chim. Acta 642 2009 171 178
23. Y. Lin, and H.H. Zhang Component selection and smoothing in multivariate nonparametric regression Ann. Statist. 34 2006 2272 2297
24. C. Linkletter, D. Bingham, N. Hengartner, D. Higdon, and K.Q. Ye Variable selection for Gaussian process models in computer experiments Technometrics 48 2006 478 490 (Pubitemid 44865389)
25. G. Marra, and S.N. Wood Practical variable selection for generalized additive models Comput. Statist. Data Anal. 55 2011 2372 2387
26. L. Meier, S. van de Geer, and P. Bühlmann High-dimensional additive modeling Ann. Statist. 37 2009 3779 3821
27. A. Miller Subset Selection in Regression second ed. Monographs on Statistics and Applied Probability vol. 95 2002 Chapman & Hall/CRC Boca Raton, FL
28. P. Ravikumar, J. Lafferty, H. Liu, and L. Wasserman Sparse additive models J. R. Stat. Soc. Ser. B Stat. Methodol. 71 2009 1009 1030
29. B.J. Reich, C.B. Storlie, and H.D. Bondell Variable selection in Bayesian smoothing spline ANOVA models: application to deterministic computer codes Technometrics 51 2009 110 120
30. G. Schwarz Estimating the dimension of a model Ann. Statist. 6 1978 461 464
31. P. Shi, and C.L. Tsai Semiparametric regression model selections J. Statist. Plann. Inference 77 1999 119 139
32. T.S. Shively, R. Kohn, and S. Wood Variable selection and function estimation in additive nonparametric regression using a data-based prior J. Amer. Statist. Assoc. 94 1999 777 806
33. Z. Shun, and P. McCullagh Laplace approximation of high-dimensional integrals J. R. Stat. Soc. Ser. B Stat. Methodol. 57 1995 749 760
34. C.J. Stone Additive regression and other nonparametric models Ann. Statist. 13 1985 689 705
35. R. Tibshirani Regression shrinkage and selection via the Lasso J. R. Stat. Soc. Ser. B Stat. Methodol. 58 1996 267 288
36. G. Wahba Spline Models for Observational Data CBMS-NSF Regional Conference Series in Applied Mathematics vol. 59 1990 Society for Industrial and Applied Mathematics (SIAM) Philadelphia, PA
37. S. Wood, R. Kohn, T. Shively, and W. Jiang Model selection in spline nonparametric regression J. R. Stat. Soc. Ser. B Stat. Methodol. 64 2002 119 139
38. M. Yuan, and Y. Lin Efficient empirical Bayes variable selection and estimation in linear models J. Amer. Statist. Assoc. 100 2005 1215 1225 (Pubitemid 41801270)
39. M. Yuan, and Y. Lin Model selection and estimation in regression with grouped variables J. R. Stat. Soc. Ser. B Stat. Methodol. 68 2006 49 67 (Pubitemid 43415335)
40. H. Zou The adaptive Lasso and its oracle properties J. Amer. Statist. Assoc. 101 2006 1418 1429
41. H. Zou, and T. Hastie Regularization and variable selection via the elastic net J. R. Stat. Soc. Ser. B Stat. Methodol. 67 2005 301 320 (Pubitemid 40465877)