Bayesian smoothing with gaussian processes using fourier basis functions in the spectralGP package

Journal of Statistical Software

Volumn 19, Issue 2, 2007, Pages 1-38

  Paciorek, Christopher J ^a  

^a HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Bayesian statistics; FFT; Fourier basis; Generalized additive model; Generalized linear mixed model; Geostatistics; Markov chain Monte Carlo; Spatial statistics; Spectral representation

Indexed keywords

EID: 34247197120     PISSN: 15487660     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v019.i02     Document Type: Article

References (49)

1. Banerjee S, Carlin B, Carlin A (2004). Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall.
2. Berger JO, De Oliveira V, Sansó B (2001). "Objective Bayesian Analysis of Spatially Correlated Data." Journal of the American Statistical Association, 96(456), 1361-1374.
3. Booth JG, Hubert JP (1999). "Maximizing Generalized Linear Mixed Model Likelihoods with an Automated Monte Carlo EM Algorithm." Journal of the Royal Statistical Society B, 61, 265-285.
4. Borgman L, Taheri M, Hagan R (1984). "Three-dimensional, Frequency-domain Simulations of Geological Variables." In G Verly (ed.), "Geostatistics for Natural Resources Characterization, Part 1," pp. 517-541. D. Reidel Publishing Company.
5. Christensen O, Møller J, Waagepetersen R (2000). "Analysis of Spatial Data Using Generalized Linear Mixed Models and Langevin-type Markov Chain Monte Carlo." Technical Report R-002009, Department of Mathematics, Aalborg University. URL http: //www.math.auc.dk/~rw/publications. html.
6. Christensen O, Roberts G, Skold M (2006). "Robust Markov Chain Monte Carlo Methods for Spatial Generalized Linear Mixed Models." Journal of Computational and Graphical Statistics, 15, 1-17.
7. Christensen OF, Waagepetersen R (2002). "Bayesian Prediction of Spatial Count Data Using Generalized Linear Mixed Models." Biometrics, 58, 280-286.
8. Cowles MK, Carlin BP (1996). "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review." Journal of the American Statistical Association, 91, 883-904.
9. Cressie N (1993). Statistics for Spatial Data. Wiley-Interscience, New York, revised edition.
10. Diggle PJ, Tawn JA, Moyeed RA (1998). "Model-based Geostatistics." Applied Statistics, 47, 299-326.
11. Dudgeon D, Mersereau R (1984). Multidimensional Digital Signal Processing. Prentice Hall, Englewood Cliffs, New Jersey.
12. Furrer R, Genton MG, Nychka D (2006). "Covariance Tapering for Interpolation of Large Spatial Datasets." Journal of Computational and Graphical Statistics, 15, 502-523.
13. Gelfand A, Sahu S, Carlin B (1996). "Efficient Parametrizations for Generalized Linear Mixed Models." In J Bernardo, J Berger, A Dawid, A Smith (eds.), "Bayesian Statistics 5," pp. 165-180.
14. Gelman A (2006). "Prior Distributions for Variance Parameters in Hierarchical Models (Comment on Browne and Draper Article)." Bayesian Analysis, 1(3), 515-534.
15. Gibbons RD, Hedeker D (1997). "Random Effects Probit and Logistic Regression Models for Three-level Data." Biometrics, 53, 1527-1537.
16. Green P (1995). "Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination." Biometrika, 82, 711-732.
17. Hastie TJ, Tibshirani RJ (1990). Generalized Additive Models. Chapman & Hall Ltd, London. ISBN 0412343908.
18. Heagerty PJ, Lele SR (1998). "A Composite Likelihood Approach to Binary Spatial Data." Journal of the American Statistical Association, 93, 1099-1111.
19. Heagerty PJ, Lumley T (2000). "Window Subsampling of Estimating Functions with Application to Regression Models." Journal of the American Statistical Association, 95(449), 197-211.
20. Hedeker D, Gibbons RD (1994). "A Random-Effects Ordinal Regression Model for Multilevel Analysis." Biometrics, 50, 933-944.
21. Higdon D, Swall J, Kern J (1999). "Non-stationary Spatial Modeling." In J Bernardo, J Berger, A Dawid, A Smith (eds.), "Bayesian Statistics 6," pp. 761-768. Oxford University Press, Oxford, U.K.
22. Hwang JN, Lay SR, Maechler M, Martin D, Schimert J (1994). "Regression Modeling in Backpropagation and Projection Pursuit Learning." IEEE Transactions on Neural Networks, 5, 342-353.
23. Kammann E, Wand M (2003). "Geoadditive Models." Applied Statistics, 52, 1-18.
24. Laslett GM (1994). "Kriging and Splines: An Empirical Comparison of Their Predictive Performance in Some Applications (Disc: P 401-409)." Journal of the American Statistical Association, 89, 391-400.
25. Matsuo T, Paul D, Nychka D (2006). "Nonstationary Covariance Modeling for Incomplete Data: Smoothed Monte Carlo EM Approach." Submitted.
26. McCulloch CE (1994). "Maximum Likelihood Variance Components Estimation for Binary Data." Journal of the American Statistical Association, 89, 330-335.
27. McCulloch CE (1997). "Maximum Likelihood Algorithms for Generalized Linear Mixed Models." Journal of the American Statistical Association, 92, 162-170.
28. McCulloch CE, Searle SR (2001). Generalized, Linear, and Mixed Models. John Wiley & Sons.
29. Neal R (1993). "Probabilistic Inference Using Markov Chain Monte Carlo Methods." Technical Report CRG-TR-93-1, Department of Computer Science, University of Toronto. URLhttp: //www.es.toronto.edu/~radford/papers- online.html.
30. Nychka DW (2000). "Spatial-Process Estimates as Smoothers." In M Schimek (ed.), "Smoothing and Regression: Approaches, Computation, and Application," pp. 393-424. John Wiley & Sons.
31. O'Connell M, Wolfinger R (1997). "Spatial Regression Models, Response Surfaces, and Process Optimization." Journal of Computational and Graphical Statistics, 6, 224-241.
32. Oman S, Landsman V, Carmel Y, Kadmon R (2007). "Analyzing Spatially Distributed Binary Data Using Independent-Block Estimating Equations." Biometrics. In press.
33. Paciorek C (2007). "Computational Techniques for Spatial Logistic Regression with Large Datasets." Computational Statistics and Data Analysis, 51, 3631-3653.
34. Paciorek C, McLachlan J (2007). "Long-term Vegetation Dynamics: Bayesian Inference for Spatio-temporal Trends in Forest Composition Using the Fossil Pollen Record." Technical report, Harvard University Biostatistics. Forthcoming.
35. Paciorek C, Schervish M (2006). "Spatial Modelling Using a New Class of Nonstationary Covariance Functions." Environmetrics, 17, 483-506.
36. Pintore A, Holmes C (2006). "Non-stationary Covariance Functions via Spatially Adaptive Spectra." Journal of the american Statistical Association. In review.
37. R Development Core Team (2006). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http: //www.R-proj ect.org.
38. Royle JA, Wikle CK (2005). "Efficient Statistical Mapping of Avian Count Data." Environmental and Ecological Statistics, 12(2), 225-243.
39. Rue H, Held L (2005). Gaussian Markov Random Fields: Theory and Applications. Chapman &: Hall, Boca Raton.
40. Rue H, Steinsland I, Erland S (2004). "Approximating Hidden Gaussian Markov Random Fields." Journal of the Royal Statistical Society B: Statistical Methodology, 66(4), 877-892.
41. Rue H, Tjelmeland H (2002). "Fitting Gaussian Markov Random Fields to Gaussian fields." Scandinavian Journal of Statistics, 29(1), 31-49.
42. Ruppert D, Wand M, Carroll R (2003). Semiparametric Regression. Cambridge University Press, Cambridge, U.K.
43. Shumway R, Stoffer D (2000). Time Series Analysis and its Applications. Springer-Verlag, New York.
44. Stein M (2005). "Nonstationary Spatial Covariance Functions." Technical Report 21, University of Chicago. URL http://www.stat.uchicago. edu/~cises/research/cises-tr21. pdf.
45. Stein ML, Chi Z, Welty LJ (2004). "Approximating Likelihoods for Large Spatial Data Sets." Journal of the Royal Statistical Society B: Statistical Methodology, 66(2), 275-296.
46. Wikle C (2002). "Spatial Modeling of Count Data: A Case Study in Modelling Breeding Bird Survey Data on Large Spatial Domains." In A Lawson, D Denison (eds.), "Spatial Cluster Modelling," pp. 199-209. Chapman & Hall.
47. Wood S (2004). "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models." Journal of the American Statistical Association, 99, 673-686.
48. Wood S (2006). Generalized Additive Models: An Introduction with R. Chapman & Hall, Boca Raton.
49. Zhang H (2004). "Inconsistent Estimation and Asymptotically Equal Interpolation in Modelbased Geostatistics." Journal of the American Statistical Association, 99, 250-261.