Bayesian spatio-temporal models based on discrete convolutions

Canadian Journal of Statistics

Volumn 36, Issue 2, 2008, Pages 239-258

  Sansó, Bruno ^a   Schmidt, Alexandra M ^b   Nobre, Aline A ^c  

^a University of California Santa Cruz   (United States)

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^c INSTITUTO OSWALDO CRUZ   (Brazil)

Author keywords

Bayesian inference; Gaussian process; Model comparison; Non stationarity; Nonseparability

Indexed keywords

EID: 47949125689     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.1002/cjs.5550360205     Document Type: Article

References (40)

1. S. Banerjee, B. P. Carlin & A. E. Gelfand (2004). Hierarchical Modeling and Analysis for Spatial Data. CRC Press/Chapman Hall.
2. L. M. Berliner (2000). Hierarchical Bayesian modeling in the environmental sciences. Allgemeines Statistisches Archiv/Journal of the German Statistical Society, 84, 141-153.
3. P. J. Brown, N. D. Le & J. V. Zidek (1995). Multivariate spatial interpolation and exposure to air pollutants. The Canadian Journal of Statistics, 22, 489-509.
4. C. Carter & R. Kohn (1994). On Gibbs sampling for state space models. Biometrika, 81, 541-553.
5. N. Cressie & H. Huang (1999). Classes of nonseparable, spatio-temporal stationary covariance functions. Journal of the American Statistical Association, 94, 1330-1340.
6. S. Frühwirth-Schnater (1994). Data augmentation and dynamic linear models. Journal of Time Series Analysis, 15, 183-202.
7. M. Fuentes (2002). Spectral methods for nonstationary spatial processes. Biometrika, 89, 197-210.
8. M. Fuentes & R. L. Smith (2002). A New Class of Nonstationary Spatial Models. Technical Report.
9. D. Gamerman & H. F. Lopes (2006). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition. Chapman & Hall/CRC, Boca Raton.
10. A. E. Gelfand & S. K. Ghosh (1998). Model choice: A minimum posterior predictive loss approach. Biometrika, 85, 1-11.
11. A. E. Gelfand, A. M. Schmidt, S. Banerjee & C. F. Sirmans (2004). Nonstationary multivariate process modeling through spatially varying coregionalization. Test, 13, 263-312.
12. T. Gneiting (2002). Nonseparable, stationary covariance functions for space-time data. Journal of the American Statistical Association, 97, 590-600.
13. D. Higdon (2002). Space and space-time modeling using process convolutions. In Quantitative Methods for Current Environmental Issues (C. W. Anderson, V. Barnett, P. C. Chatwin & A. H. El-Shaarawi, eds.), Springer-Verlag, London, pp. 37-56.
14. D. Higdon, J. Swall & J. Kern (1999). Non-stationary spatial modelling. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, P. Dawid & A. F. M. Smith, eds.), Oxford University Press, pp. 761-768.
15. N. J. Higham (1996). Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia.
16. G. Huerta & M. West (1999). Priors and component structures in autoregressive time series models. Journal of the Royal Statistical Society, 61, 881-899.
17. S. Kim, N. Shephard & S. Chib (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Financial Studies, 65, 361-393.
18. H. K. H. Lee, C. H. Holloman, C. A. Calder & D. M. Higdon (2002). Flexible Gaussian processes via convolutions. Technical Report 02-09, Institute of Statistics and Decision Sciences, Duke University, Durham, North Carolina.
19. F. Liu (2000). Bayesian time series: Analysis methods using simulation based computation. Technical Report, Institute of Statistics and Decision Sciences, Duke University, Durham, North Carolina.
20. W. Meiring, P. Guttorp & P. D. Sampson (1998). Space-time estimation of grid-cell hourly ozone levels for assessment of a deterministic model. Environmental and Ecological Statistics, 5, 197-222.
21. J. F. Monahan (1984). A note on enforcing stationarity in autoregressive moving average models. Biometrika, 71, 403-404.
22. R. J. Muirhead (1982). Aspects of Multivariate Statistical Theory. Wiley, New York.
23. P. Müller, B. Sansó & M. De Iorio (2004). Optimal Bayesian design by inhomogenous Markov chain simulation. Journal of the American Statistical Association, 99, 788-798.
24. A. A. Nobre (2007). Spatio-temporal Models Based on Multivariate Auto-regressive Processes (in Portuguese). Doctoral dissertation, Department of Statistical Methods - IM, UFRJ, Rio de Janeiro, RJ, Brazil.
25. C. J. Paciorek & M. J. Schervish (2004). Nonstationary covariance functions for Gaussian process regression. Advances in Neural Information Processing Systems, 16, 273-280.
26. M. B. Priestley (1981). Spectral Analysis and Time Series. Academic Press, San Diego.
27. M. Rosenblatt (1952). Remarks on a multivariate transformation. The Annals of Mathematical Statistics, 23, 470-472.
28. J. A. Royle & L. M. Berliner (1999). A hierarchical approach to multivariate spatial modeling and prediction. Journal of Agricultural, Biological and Environmental Statistics, 4, 29-56.
29. B. Sansó & L. Guenni (2000). A nonstationary multisite model for rainfall. Journal of the American Statistical Association, 95, 1064-1089.
30. M. A. Snyder, B. Sansó & L. C. Sloan (2007). Validation of climate model output using Bayesian statistical methods. Climatic Change, 83, 457-476, doi 10.1007/s10584-007-9262-3.
31. M. L. Stein (1999). Interpolation of Spatial Data. Springer-Verlag, New York.
32. M. L. Stein (2005). Space-time covariance functions. Journal of the American Statistical Association, 100, 310-321.
33. H. V. Storch (1999). Statistical Analysis in Climate Research. Cambridge University Press.
34. J. Stroud, P. Müller & B. Sansó (2001). Dynamic models for spatio-temporal data. Journal of the Royal Statistical Society, 63, 673-689.
35. H. Uhlig (1994). On singular Wishart and singular multivariate beta distributions. The Annals of Statistics, 22, 395-405.
36. H. Wackernagel (2001). Multivariate Geostatistics - An Introduction with Applications, Second Edition. Springer-Verlag, New York.
37. M. West & J. Harrison (1997). Bayesian Forecasting and Dynamic Models, Second Edition. Springer-Verlag, New York.
38. P. Whittle (1954). On stationary processes in the plane. Biometrika, 41, 434-449.
39. C. K. Wikle, L. M. Berliner & N. Cressie (1998). Hierarchical Bayesian space-time models. Environmental and Ecological Statistics, 5, 117-154.
40. C. K. Wikle & N. Cressie (1999). A dimension-reduction approach to space-time Kalman filtering. Biometrika, 86, 815-829.