Asymptotic models and inference for extremes of spatio-temporal data

Extremes

Volumn 13, Issue 4, 2010, Pages 375-397

  Turkman, Kamil Feridun ^a   Amaral Turkman, M A ^a   Pereira, J M ^b  

^a UNIVERSITY OF LISBON   (Portugal)

^b INSTITUTO SUPERIOR DE AGRONOMIA   (Portugal)

Author keywords

Bayesian hierarchical models; Generalized Pareto distribution; Wildfires

Indexed keywords

EID: 79451471191     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-009-0092-8     Document Type: Article

References (29)

1. Albin, P.: On extremal theory for non differentiable stationary processes. Ph. D. thesis, Dept. of Mathematical Statistics, University of Lund (1987).
2. Albin, P.: On extremal theory for stationary processes. Ann. Probab. 18, 92-128 (1990).
3. Banerjee, S., Carlin, B. P., Gelfand, A.: Hierarchical Modelling and Analysis for Spatial Data. Chapman and Hall (2004).
4. Buishand, A., de Haan, L., Zhou, C.: On spatial extremes: with application to a rainfall problem. Ann. Appl. Stat. 2, 624-642 (2008).
5. Castellanos, M. E., Cabras, S.: A default Bayesian procedure for the generalized Pareto distribution. J. Stat. Plan. Inference 137, 473-483 (2006).
6. Chavez-Demoulin, V., Davison, A.: Generalized additive modelling of sample extremes. Appl. Stat. 54, 207-222 (2005).
7. 10 pollution. Atmos. Environ. 41, 532-542 (2007).
8. Coles, S.: An Introduction to Statistical Modelling of Extreme Values. Springer, New York (2001).
9. Coles, S., Tawn, J.: Modelling extremes of the areal rainfall process. J. R. Stat. Soc. B 58, 329-347 (1996).
10. Cooley, D., Naveau, P., Joneli, V., Rababtel, A., Grancher, D.: A Bayesian hierarchical extreme value model for lichenometry. Environmetrics 17, 555-574 (2006).
11. Cooley, D., Nychka, D., Naveau, P.: Bayesian spatial model of extreme precipitation return levels. JASA 102, 824-840 (2007).
12. de Haan, L., Ferreira, A.: Extreme Value Theory, An Introduction. Springer, New York (2006).
13. de Haan, L., Pereira, T.: Spatial extremes: models for the stationary case. Ann. Stat. 34, 146-168 (2006).
14. de Zea Bermudez, P., Mendes, J., Pereira, J. M. C., Turkman, K. F., Vasconcelos, M. J. P.: Spatial and temporal extremes of wildfire sizes in Portugal (1984-2004). Int. J. Wildland Fire (2009, in press).
15. Fawcett, L., Walshaw, D.: A hierarchical model for extreme wind speeds. Appl. Stat. 55, 631-646 (2006).
16. Fougères, A. L., Nolan, J. P., Rootzén, H.: Models for dependent extremes using stable mixtures. Scand. J. Statist. 36, 42-59 (2009).
17. Gelman, A., Pardoe, I.: Bayesian measures of explained variance and pooling in multilevel models. Technometrics 40, 241-251 (2005).
18. Heffernan, J. E., Tawn, J.: A conditional approach for multivariate extreme values. J. R. Stat. Soc. B 66, 497-546 (2004).
19. Kabluchko, Z., Schlather, M., de Haan, L.: Stationary Max-stable fields associated to negative definite functions. Ann. Probab. www. arxiv. org (2009).
20. Leadbetter, M. R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, New York (1983).
21. Lunn, D. J., Thomas, A., Best, N., Spiegelhalter, D.: WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Stat. Comput. 10, 325-337 (2000).
22. Mendes J. M., de Zea Bermudez P., Pereira J. M. C., Turkman K. F., Vasconcelos, M. J. P.: Spatial extremes of wildfire sizes: Bayesian hierarchical models for extremes. Environ. Ecol. Stat. doi: 10. 1007/s10651-008-0099-3 (2008).
23. Padoan, S. A., Ribatet, M., Sisson, S. A.: Likelihood-based inference for max-stable processes. JASA (Theory and Methods) (2009, submitted).
24. Piterbarg, V.: Asymptotic Methods in the Theory of Gaussian Processes and Fields. AMS Monographs (1996).
25. Reed, W. J., McKelvey, K. S.: Power-law behaviour and parametric models for the size-distribution of forest fires. Ecol. Model. 150, 239-254 (2002).
26. Ribatet, M.: A User's Guide to the SpatialExtremes Package. École Polytechnique Fédérale de Lausanne, Switzerland (2009).
27. Sang, H.: Extreme value modeling for space-time data with meteorological applications. Ph. D. thesis, Duke University (2008).
28. Schlather, M.: Models for stationary max-stable random fields. Extremes 5, 33-44 (2002).
29. Thomas, A., Best, N., Lunn, D., Arnold, R., Spiegelhalter, D.: GeoBUGS User Manual Version 1. 2 (2004).