spikeSlabGAM: Bayesian variable selection, model Choice and regularization for generalized additive mixed models in R

Journal of Statistical Software

Volumn 43, Issue 14, 2011, Pages 1-24

  Scheipl, Fabian ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

MCMC; Normal inverse gamma; P splines; Spike and slab prior

Indexed keywords

EID: 80052986293     PISSN: None     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v043.i14     Document Type: Article

References (36)

1. Bae K, Mallick BK (2004). Gene Selection Using a Two-Level Hierarchical Bayesian Model. Bioinformatics, 20(18), 3423-3430.
2. Baglama J, Reichel L (2006). Augmented Implicitly Restarted Lanczos Bidiagonalization Methods. SIAM Journal on Scientific Computing, 27(1), 19-42.
3. Baglama J, Reichel L, Lewis BW (2011). Irlba: Fast Partial SVD by Implicitly-Restarted Lanczos Bidiagonalization. R package version 1.0.0, URL http://CRAN.R-project.org/package=irlba.
4. Brezger A, Kneib T, Lang S (2005). BayesX: Analyzing Bayesian Structural Additive Re- gression Models. Journal of Statistical Software, 14(11). URL http://www.jstatsoft.org/v14/i11/.
5. Carvalho CM, Polson NG, Scott JG (2010). The Horseshoe Estimator for Sparse Signals. Biometrika, 97(2), 465-480.
6. Cottet R, Kohn RJ, Nott DJ (2008). Variable Selection and Model Averaging in Semi-parametric Overdispersed Generalized Linear Models. Journal of the American Statistical Association, 103(482), 661-671.
7. Fahrmeir L, Kneib T, Konrath S (2010). Bayesian Regularisation in Structured Additive Regression: a Unifying Perspective on Shrinkage, Smoothing and Predictor Selection. Statistics and Computing, 20(2), 203-219.
8. Fahrmeir L, Kneib T, Lang S (2004). Penalized Structured Additive Regression for SpaceTime Data: a Bayesian Perspective. Statistica Sinica, 14, 731-761.
9. Frank A, Asuncion A (2010). UCI Machine Learning Repository. URL http://archive.ics.uci.edu/ml/.
10. Frühwirth-Schnatter S, Wagner H (2010). Bayesian Variable Selection for Random Intercept Modelling of Gaussian and Non-Gaussian Data. In JM Bernardo, MJ Bayarri, JO Berger, AP Dawid, D Heckerman, AFM Smith, M West (eds.), Bayesian Statistics 9. Oxford Uni- versity Press.
11. Gelman A, Van Dyk DA, Huang Z, Boscardin JW (2008). Using Redundant Parameterizations to Fit Hierarchical Models. Journal of Computational and Graphical Statistics, 17(1),95-122.
12. George EI, McCulloch RE (1993). Variable Selection via Gibbs Sampling. Journal of the American Statistical Association, 88(423), 881-889.
13. Gu C (1992). Diagnostics for Nonparametric Regression Models with Additive Terms. Journal of the American Statistical Association, 87(420), 1051-1058.
14. Han C, Carlin BP (2001). Markov Chain Monte Carlo Methods for Computing Bayes Factors. Journal of the American Statistical Association, 96(455), 1122-1132.
15. Hothorn T, Buehlmann P, Kneib T, Schmid M, Hofner B (2011). Mboost: Model-Based Boosting. R package version 2.0-12, URL http://CRAN.R-project.org/package=mboost.
16. Ishwaran H, Rao JS (2005). Spike and Slab Variable Selection: Frequentist and Bayesian Strategies. The Annals of Statistics, 33(2), 730-773.
17. Kneib T (2006). Mixed Model Based Inference in Structured Additive Regression. Dr. Hut Verlag. URL http://edoc.ub.uni-muenchen.de/archive/00005011/.
18. Lang S, Brezger A (2004). Bayesian P-Splines. Journal of Computational and Graphical Statistics, 13(1), 183-212.
19. Leisch F, Dimitriadou E (2010). Mlbench: Machine Learning Benchmark Problems. R pack- age version 2.1-0, URL http://CRAN.R-project.org/package=mlbench.
20. Lin Y, Zhang HH (2006). Component Selection and Smoothing in Multivariate Nonparametric Regression. The Annals of Statistics, 34(5), 2272-2297.
21. Meng XL, van Dyk D (1997). The EM Algorithm - An Old Folk-Song Sung to a Fast New Tune. Journal of the Royal Statistical Society B, 59(3), 511-567.
22. Mitchell TJ, Beauchamp JJ (1988). Bayesian Variable Selection in Linear Regression. Journal of the American Statistical Association, 83(404), 1023-1032.
23. Polson NG, Scott JG (2010). Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction. In JM Bernardo, MJ Bayarri, JO Berger, AP Dawid, D Heckerman, AFM Smith, M West (eds.), Bayesian Statistics 9. Oxford University Press.
24. R Development Core Team (2011). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/.
25. Reich BJ, Storlie CB, Bondell HD (2009). Variable Selection in Bayesian Smoothing Spline ANOVA Models: Application to Deterministic Computer Codes. Technometrics, 51(2), 110.
26. Rue H, Held L (2005). Gaussian Markov Random Fields: Theory and Applications. Chapman & Hall.
27. Scheipl F (2010). Normal-Mixture-of-Inverse-Gamma Priors for Bayesian Regularization and Model Selection in Generalized Additive Models. Technical Report 84, Department of Statistics, LMU München. URL http://epub.ub.uni-muenchen.de/11785/.
28. Scheipl F (2011). Bayesian Regularization and Model Choice in Structured Additive Regres-sion. Dr. Hut Verlag. URL http://edoc.ub.uni-muenchen.de/13005/.
29. Sturtz S, Ligges U, Gelman A (2005). R2WinBUGS: A Package for Running WinBUGS from R. Journal of Statistical Software, 12(3), 1-16. URL http://www.jstatsoft.org/v12/i03/.
30. Tierney L, Rossini AJ, Li N, Sevcikova H (2011). Snow: Simple Network Of Workstations. R package version 0.3-7, URL http://CRAN.R-project.org/package=snow.
31. Urbanek S (2011). Multicore: Parallel Processing of R Code on Machines with Multiple Cores or CPUs. R package version 0.1-6, URL http://CRAN.R-project.org/package=multicore.
32. Wahba G, Wang Y, Gu C, Klein R, Klein B (1995). Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic Retinopathy. The Annals of Statistics, 23(6), 1865-1895.
33. Wickham H (2009). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag, New York. URL http://had.co.nz/ggplot2/book.
34. Wood S, Kohn R, Shively T, Jiang W (2002). Model Selection in Spline Nonparametric Regression. Journal of the Royal Statistical Society B, 64(1), 119-139.
35. Wood SN (2006). Generalized Additive Models: An Introduction with R. CRC Press.
36. Yau P, Kohn R, Wood S (2003). Bayesian Variable Selection and Model Averaging in High-Dimensional Multinomial Nonparametric Regression. Journal of Computational and Graphical Statistics, 12(1), 23-54.