Bayesian curve-fitting with free-knot splines

Biometrika

Volumn 88, Issue 4, 2001, Pages 1055-1071

  Dimatteo, Ilaria ^a   Genovese, Christopher R ^a   Kass, Robert E ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

BIC; Generalised linear model; Nonparametric regression; Reversible jump Markov chain Monte Carlo; Smoothing; Unit information prior

Indexed keywords

EID: 0010045457     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/88.4.1055     Document Type: Article

References (21)

1. BILLER, C. (2000). Adaptive Bayesian regression splines in semiparametric generalized linear models. J. Comp. Graph. Statist. 9, 122-40.
2. DENISON, D. O. T., MALLICK, B. K. & SMITH, A. F. M. (1998). Automatic Bayesian curve fitting. J. R. Statist. Soc. B 60, 330-50.
3. EILERS, P. H. C. & MARX, B. D. (1996). Flexible smoothing with B-splines and penalties (with Discussion). Statist. Sci. 11, 89-121.
4. EVANS, M. & SWARTZ, T. (1995). Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems. Statist. Sci. 10, 254-72.
5. GENOVESE, C. R. (2000). A Bayesian time-course model for functional Magnetic Resonance Imaging data. J. Am. Statist. Assoc. 95, 691-719.
6. GREEN, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-32.
7. HALPERN, E. F. (1973). Bayesian spline regression when the number of knots is unknown. J. R. Statist. Soc. B 35, 347-60.
8. HANSEN, M. H. & KOOPERBERG, C. (2001). Spline adaptation in extended linear models. Statist. Sci. To appear.
9. HASTIE, T. J. & TIBSHIRANI, R. J. (1990). Generalized Additive Models. London: Chapman and Hall.
10. KASS, R. E. & VENTURA, V. (2001). A spike train probability model. Neural Comp. 13, 1713-20.
11. KASS, R. E. & WASSERMAN, L. (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. J. Am. Statist. Assoc. 90, 928-34.
12. LINDSTROM, M. J. (1999). Penalized estimation of free-knot splines. J. Comp. Graph. Statist. 8, 333-52.
13. LIU, J. S., WONG, W. H. & KONG, A. (1994). Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika 81, 27-40.
14. MCCULLAGH, P. & NELDER, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman and Hall.
15. OLSON, C. R. & ROLLENHAGEN, J. E. (1999). Low-frequency oscillations in Macaque IT cortex during competitive interactions between stimuli. Soc. Neurosci. Abstr. 25, 916.
16. PAULER, D. K. (1998). The Schwarz criterion and related methods for normal linear models. Biometrika 85, 13-27.
17. SMITH, M. & KOHN, R. (1996). Nonparametric regression using Bayesian variable selection. J. Economet. 75, 317-43.
18. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with Discussion). Aim. Statist. 22, 1701-62.
19. VENTURA, V., CARTA, R., KASS, R. E., GETTNER, S. & OLSON, C. R. (2001). Statistical analysis of temporal evolution in single-neuron firing rates. Biostatistics 2. To appear.
20. WAHBA, G. (1990). Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.
21. ZHOU, S. & SHEN, X. (2001). Spatially adaptive regression splines and accurate knot selection schemes. J. Am. Statist. Assoc. 96, 247-59.