Bayesian P-Splines

Journal of Computational and Graphical Statistics

Volumn 13, Issue 1, 2004, Pages 183-212

  Lang, Stefan ^a   Brezger, Andreas ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Geoadditive models; Locally adaptive smoothing parameters; MCMC; Surface fitting; Varying coefficient models

Indexed keywords

EID: 1842591298     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/1061860043010     Document Type: Article

References (41)

1. Albert, J. H., and Chib, S. (1993), "Bayesian Analysis of Binary Polychotomous Response Data," Journal of the American Statistical Association, 88, 669-679.
2. Besag, J., and Higdon, D. (1999), "Bayesian Analysis of Agricultural Field Experiments," Journal of the Royal Statistical Society, Ser. B, 61, 691-746.
3. Besag, J., and Kooperberg, C. (1995), "On Conditional and Intrinsic Autoregressions," Biometrika, 82, 733-746.
4. Besag, J., York, Y., and Mollie, A. (1991), "Bayesian Image Restoration with two Applications in Spatial Statistics" (with discussion), Annals of the Institute of Statistical Mathematics, 43, 1-59.
5. Biller, C. (2000), "Adaptive Bayesian Regression Splines in Semiparametric Generalized Linear Models," Journal of Computational and Graphical Statistics, 12, 122-140.
6. Breiman, L., and Friedman, J. (1985), "Estimating Optimal Transformations for Multiple Regression and Correlation," Journal of the American Statistical Association, 80, 580-598.
7. Carter, C., and Kohn, R. (1994), "On Gibbs Sampling for State Space Models," Biometrika, 81, 541-553.
8. Chen, Z. (1993), "Fitting Multivariate Regression Functions by Interaction Spline Models," Journal of the Royal Statistical Society, Ser. B, 55, 473-491.
9. Clayton, D. (1996), "Generalized Linear Mixed Models," in Markov Chain Monte Carlo in Practice, eds. R. S. Gilks et al., London: Chapman and Hall, pp. 275-301.
10. Cleveland, W., and Grosse, E. (1991), "Computational Methods for Local Regression," Statistics and Computing, 1, 47-62.
11. De Boor, C. (1978), A Practical Guide to Splines, New York: Springer-Verlag.
12. Denison, D., Mallick, B., and Smith, A. (1998), "Automatic Bayesian Curve Fitting," Journal of the Royal Statistical Society, Ser. B, 60, 333-350.
13. Di Matteo, I., Genovese, C. R., and Kass, R. E. (2001), "Bayesian Curve-Fitting with Free-Knot Splines," Biometrika, 88, 1055-1071.
14. Eilers, P., and Marx, B. (1996), "Flexible Smoothing using B-splines and Penalized Likelihood" (with comments and rejoinder), Statistical Science, 11, 89-121.
15. Fahrmeir, L., and Lang, S. (2001a), "Bayesian Inference for Generalized Additive Mixed Models Based on Markov Random Field Priors," Journal of the Royal Statistical Society, Ser. C, 50, 201-220.
16. _ (2001b), "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, 53, 11-30.
17. Fahrmeir, L., and Tutz, G. (2001), Multivariate Statistical Modelling Based on Generalized Linear Models (2 ed.), New York: Springer.
18. Friedman, J. (1991), "Multivariate Adaptive Regression Splines" (with discussion), The Annals of Statistics, 19, 1-141.
19. George, A., and Liu, J. W. (1981), Computer Solution of Large Sparse Positive Definite Systems, Englewood Cliffs, NJ: Prentice-Hall.
20. Gössl, C. (2001), Bayesian Models in Functional Magnetic Resonance Imaging: Approaches for Human Brain Mapping, Aachen: Shaker Verlag.
21. Gössl, C., Auer, D., and Fahrmeir, L. (2000), "Dynamic Models in fMRI," Magnetic Resonance in Medicine, 43, 72-81.
22. Hansen, M. H., and Kooperberg, C. (2002), "Spline Adaptation in Extended Linear Models," Statistical Science, 17, 2-51.
23. Hastie, T., and Tibshirani, R. (1990), Generalized Additive Models, London: Chapman and Hall.
24. _ (1993), "Varying-Coefficient Models," Journal of the Royal Statistical Society, Ser. B, 55, 757-796.
25. _ (2000), "Bayesian Backfitting," Statistical Science, 15, 193-223.
26. Hastie, T., Tibshirani, R., and Friedman, J. (2001), The Elements of Statistical Learning, New York: Springer-Verlag.
27. Hobert, J., and Casella, G. (1996), "The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models," Journal of the American Statistical Association, 91, 1461-1473.
28. Kamman, E., and Wand, M. (2003), "Geoadditive Models," Journal of the Royal Statistical Society, Ser. C, 52, 1-18.
29. Knorr-Held, L. (1999), "Conditional Prior Proposals in Dynamic Models," Scandinavian Journal of Statistics, 26, 129-144.
30. Lange, N. (1996), "Statistical Approaches To Human Brain Mapping By Functional Magnetic Resonance Imaging," Statistics in Medicine, 15, 389-428.
31. Luo, Z., and Wahba, G. (1997), "Hybrid Adaptive Splines," Journal of the American Statistical Association, 92, 107-116.
32. Mallick, B., Denison, D., and Smith, A. (2000), "Semiparametric Generalized Linear Models: Bayesian Approaches," in Generalized Linear Models: A Bayesian Perspective, eds. D. Dey, S. Ghosh, and B. K. Mallick, New York: Marcel-Dekker.
33. Marx, B. D., and Eilers, P. H. C. (1998), "Direct Generalized Additive Modeling with Penalized Likelihood," Computational Statistics and Data Analysis, 28, 193-209.
34. Rue, H. (2001), "Fast Sampling of Gaussian Markov Random Fields with Applications," Journal of the Royal Statistical Society, Ser. B, 63, 325-338.
35. Ruppert, D., and Carroll, R. J. (2000), "Spatially Adaptive Penalties for Spline Fitting," Australian and New Zealand Journal of Statistics, 42, 205-223.
36. Smith, M., and Kohn, R. (1996), "Nonparametric Regression using Bayesian Variable Selection," Journal of Econometrics, 75, 317-343.
37. _ (1997), "A Bayesian Approach to Nonparametric Bivariate Regression," Journal of the American Statistical Association, 92, 1522-1535.
38. Spiegelhalter, D., Best, N., Carlin, B., and van der Linde, A. (2002), "Bayesian Measures of Model Complexity and Fit," Journal of the Royal Statistical Society, Ser. B, to appear.
39. Stone, C., Hansen, M., Kooperberg, C., and Truong, Y. (1997), "Polynomial Splines and their Tensor Products in Extended Linear Modeling" (with discussion), The Annals of Statistics, 25, 1371-1470.
40. Wand, M. (2000), "A Comparision of Regression Spline Smoothing Procedures," Computational Statistics, 15, 443-462.
41. Wood, S. N. (2000), "Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties," Journal of the Royal Statistical Society, Ser. B, 62, 413-428.