Fully Bayesian spline smoothing and intrinsic autoregressive priors

Biometrika

Volumn 90, Issue 2, 2003, Pages 289-302

  Speckman, Paul L ^a   Sun, Dongchu ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Autoregressive Gaussian process; Gibbs sampling; Linear mixed model; Multivariate normal; Penalised likelihood methods; Spatial correlation; Spline smoothing

Indexed keywords

EID: 3843151334     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/90.2.289     Document Type: Article

References (31)

1. ANSLEY, C. F. & KOHN, R. (1985). Estimation, filtering, and smoothing in state space model with incompletely specified initial conditions. Ann. Statist. 13, 1286-316.
2. BERGER, J. O. & BERNARDO, J. M. (1989). Estimating a product of means: Bayesian analysis with reference priors. J. Am. Statist. Assoc. 84, 200-7.
3. BERGER, J. O. & BERNARDO, J. M. (1992). Reference priors in a variance components problem. In Bayesian Analysis in Statistics and Econometrics, Ed. P. K. Goel and N. S. Iyengar, pp. 177-94. Berlin: Springer.
4. BESAG, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with Discussion). J. R. Statist. Soc. 3 36, 192-236.
5. BESAG, J. & KOOPERBERG, C. (1995). On conditional and intrinsic autoregressions. Biometrika 82, 733-46.
6. BESAG, J., YORK., J. & MOLLIÉ, A. (1991). Bayesian image restoration, with two applications in spatial statistics (with Discussion). Ann. Inst. Statist. Math. 42, 1-59.
7. CARTER, C. K. & KOHN, R. (1994). On Gibbs sampling for state space models. Biometrika 81, 541-53.
8. CARTER, C. K. & KOHN, R. (1996). Markov chain Monte Carlo in conditionally Gaussian state space models. Biometrika 83, 589-601.
9. EUBANK, R. L. (1988). Spline Smoothing and Nonparametric Regression. New York: Marcel Dekker.
10. FAHRMEIR, L. & LANG, S. (2001). Bayesian inference for generalized additive mixed models based on Markov random field priors. Appl. Statist. 50, 201-20.
11. FAHRMEIR, L. & WAGENPFEIL, S. (1996). Smoothing hazard functions and time-varying effects in discrete duration and competing risks models. J. Am. Statist. Assoc. 91, 1584-94.
12. FAN, J. & GIJBELS, I. (1996). Local Polynomial Modeling and its Applications. London: Chapman & Hall.
13. GELFAND, A. E. & SMITH, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Am. Statist. Assoc. 85, 398-409.
14. GEMAN, S. & GEMAN, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pat. Anal. Mach. Intel. 6, 721-41.
15. GHOSH, M., NATARAJAN, K., STROUD, T. W. F. & CARLIN, B. P. (1998). Generalized linear models for small area estimation. J. Am. Statist. Assoc. 93, 273-82.
16. GU, C. (2002). Smoothing Spline ANOVA Models. New York: Springer-Verlag.
17. HOBERT, J. P. & CASELLA, G. (1996). The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. J. Am. Statist. Assoc. 91, 1461-73.
18. KIMELDORF, G. S. & WAHBA, G. (1970). A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Ann. Math. Statist. 41, 495-502.
19. KOHN, R. & ANSLEY, C. F. (1987). A new algorithm for spline smoothing based on smoothing a stochastic process. SIAM J. Sci. Statist. Comp. 8, 33-48.
20. KÜNSCH, H. R. (1987). Intrinsic autoregressions and related models on the two-dimensional lattice. Biometrika 74, 517-24.
21. REINSCH, C. (1967). Smoothing by spline functions. Numer. Math. 10, 177-83.
22. SPECKMAN, P. L. (1985). Spline smoothing and optimal rates of convergence in nonparametric regression models. Ann. Statist. 13, 970-83.
23. SUN, D., TSUTAKAWA, R. K. & SPECKMAN, P. L. (1999). Posterior distribution of hierarchical models using CAR(1) distributions. Biomeirika 86, 341-50.
24. VAN DER LINDE, A. (1995). Splines from a Bayesian point of view. Test 4, 63-81.
25. VAN DER LINDE, A. (2000). Reference priors for shrinkage and smoothing parameters. J. Statist. Plan. Infer. 90, 245-74.
26. WAHBA, G. (1978). Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. R. Statist. Soc. B 40, 364-72.
27. WAHBA, G. (1983). Bayesian 'confidence intervals' for the cross-validated smoothing spline. J. R. Statist. Soc. B 45, 133-50.
28. WAHBA, G. (1990). Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.
29. WALLER, L. A., CARLIN, B. P., XIA, H. & GELFAND, A. E. (1997). Hierarchical spatio-temporal mapping of disease rates. J. Am. Statist. Assoc. 92, 607-17.
30. WAND, M. P. & JONES, M. C. (1995). Kernel Smoothing. London: Chapman and Hall.
31. YE, K. (1994). Bayesian reference prior analysis on the ratio of variances for the balanced one-way random effect model. J. Statist. Plan. Infer. 41, 267-80.