Geostatistical Modelling Using Non-Gaussian Matérn Fields

Scandinavian Journal of Statistics

Volumn 42, Issue 3, 2015, Pages 872-890

  Wallin, Jonas ^a   Bolin, David ^b  

^a UNIVERSITY OF GOTHENBURG   (Sweden)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Laplace, Markov random fields, Mat rn covariances, MCEM algorithm, normal inverse Gaussian, SPDE, variance Gamma

Indexed keywords

EID: 84939260637     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/sjos.12141     Document Type: Article

References (29)

1. Azaïs, J.-M., Déjean S., León J.R., & Zwolska F. (2011). Transformed Gaussian stationary models for ocean waves, Probab. Eng. Mech. 26, 342-349.
2. Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae, Scand. J. Statist. 5, 151-157.
3. Berrocal, V.J., Gelfand A.E., & Holland D.M.. (2010) A spatio-temporal downscaler for output from numerical models, J. Agr. Biol. Environ. Statist. 15, 176-197.
4. Bolin, D. (2014). Spatial Matérn fields driven by non-Gaussian noise, Scand. J. Statist. 41, 557-579.
5. Bolin, D., & Lindgren F.. (2011). Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping, Ann. Appl. Statist. 5, 523-550.
6. Bolin, D., & Lindgren F. (2015). Excursion and contour uncertainty regions for latent Gaussian models, J. Roy. Statist. Soc. Ser. B Stat. Methodol. 77, 85-106.
7. Bolin, D., & Wallin, J. (2015). LANG: Tools for estimation and prediction using latent non-Gaussian models. R package version 0.1.
8. Cameletti, M., F. Lindgren, D. Simpson, & Rue H. (2013). Spatio-temporal modeling of particulate matter concentration through the SPDE approach, AStA Adv. Stat. Anal. 97, 1-23.
9. Campbell, Y.E., & T.A. Davis . (1995). Computing the sparse inverse subset: an inverse multifrontal approach. Technical Report TR-95-021, Computer and Information Sciences Department, University of Florida.
10. Cressie, N. (1993). Statistics for spatial data, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, J. Wiley, New York, USA.
11. Dempster, A.P., Laird N.M., & Rubin D.B.. (1977) Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Statist. Soc. Ser. B Stat. Methodol. 39, 1-38.
12. Diggle, P.J., & RibeiroJr, P.J. (2002). Bayesian inference in Gaussian model-based geostatistics, Geogr. Environ. Modelling 6, 129-146.
13. Eberlein, E., & von Hammerstein, E. (2004). Generalized hyperbolic and inverse Gaussian distributions: limiting cases and approximation of processes. In Seminar on stochastic analysis, random fields and applications IV, Progress in Probability, vol.58, Birkhäuser, Basel; 221-264.
14. Ferguson, T. (1967). Mathematical statistics: a decision theoretic approach, Probability and Mathematical Statistics, Academic Press, London.
15. Gneiting, T., L.I. Stanberry, E.P. Grimit, Held L., & Johnson N.A. (2008). Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds, TEST 17, 211-235.
16. Huerta, G., B. Sansó, & Stroud J.R. (2004). A spatiotemporal model for Mexico City ozone levels, J. Roy. Statist. Soc. Ser. C Appl. Statist. 53, 231-248.
17. Jørgensen, B. (1982). Statistical properties of the generalized inverse Gaussian distribution, Lecture Notes in Statistics, Springer-Verlag, New York.
18. Lindgren, F., H. Rue, & J. Lindström . An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (with discussion), J. Roy. Statist. Soc. Ser. B Stat. Methodol. 73 (2011), 423-498.
19. Matérn, B.. Spatial variation, Meddelanden från statens skogsforskningsinstitut 49 (1960), 5.
20. Matheson, J.E., & R.L. Winkler . Scoring rules for continuous probability distributions, Manage. Sci. 22(1976), 1087-1096.
21. Podgórski, K., & Wallin J. (2015). Convolution invariant generalized hyperbolic subclasses (in press), Commun. Stat..
22. R Core Team, R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2013.
23. Robert, C., & G. Casella (2004). Monte Carlo statistical methods, Springer Texts in Statistics, Springer, New York, USA.
24. Rosiński, J.. (1991). On a class of infinitely divisible processes represented as mixtures of Gaussian processes. In Stable processes and related topics, vol.25 of Progress in Probability, Birkhauser, Boston; 27-41.
25. Sahu, S.K., & Mardia K.V. (2005). A Bayesian kriged Kalman model for short-term forecasting of air pollution levels, J. Roy. Statist. Soc. Ser. C Appl. Statist. 54, 223-244.
26. Wei, G.C., & Tanner M.A. (1990). A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms, J. Amer. Statist. Assoc. 85, 699-704.
27. Whittle, P. (1963). Stochastic processes in several dimensions, Bull. Internat. Statist. Inst. 40, 974-994.
28. Wu, C. (1983). On the convergence properties of the EM algorithm, Ann. Statist. 11, 95-103.
29. Zhang, H. (2004). Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics, J. Amer. Statist. Assoc. 99, 250-261.