Abstract
Within the context of accessing the risk of forest fires, Amaral-Turkman et al. (Environ. Ecol. Stat. 18:601–617, 2011) have proposed a spatio-temporal hierarchical approach which jointly models the fire ignition probability and the fire’s size, in a Bayesian framework. This is recovered and applied to Portuguese forest fires data, with some necessary modifications in what concerns the format of the data (not available in a regular lattice over the territory) and also because of the estimation complications that arise due to the high dimensionality of the neighbouring structure involved. To address the latter, as it compromises the estimation via Markov Chain Monte Carlo (MCMC) methods, and having the model be recognized as a latent Gaussian model, it was chosen to do the Bayesian estimation also using an Integrated Nested Laplace Approximation approach, with real computational advantages. Corresponding methodologies and results are described and compared.
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References
Amaral-Turkman M.A., Turkman K.F., Le Page Y., Pereira J.M.C.: Hierarchical space-time models for fire ignition and percentage of land burned by wildfires. Environ. Ecol. Stat. 18, 601–617 (2011)
Direcção Geral dos Recursos Florestais. Resultados IFN 2005/2006. Lisboa (2006)
Gamerman D., Lopes H.F.: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd edn. Chapman & Hall/CRC, Boca Raton (2006)
Gelfand A.E., Smith F.M.: Sampling-Based Approaches to Calculating Marginal Densities. J. Am. Stat. Assoc. 85, 398–409 (1990)
Geman S., Geman D.: Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721–741 (1984)
Marques S., Borges J.G., Garcia-Gonzalo J., Moreira F., Carreiras J.M.B., Oliveira M.M., Cantarinha A., Botequim B., Pereira J.M.C.: Characterization of wildfires in Portugal. Eur. J. Forest Res. 130, 775–784 (2010)
Pereira M.G., Malamud B.D., Trigo R.M., Alves P.I.: The history and characteristics of the Portuguese rural fire database. Nat. Hazards Earth Syst. Sci. 11, 3343–3358 (2011)
Rue H., Martino S., Chopin N.: Approximate Bayesian inference for lateny Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. B. 71, 319–392 (2009)
Rundel P.W.: Landscape disturbance in Mediterranean ecosystems: an overview. In: Rundel P.W., Monenegro G., Jaksic F.M. (eds.) Landscape disturbance and biodiversity in Mediterrean- Type ecosystems, pp. 3–22. Springer, Berlin (1998)
Schoenberg F.P., Peng R., Woods J.: On the distribution of wildfire sizes. Environmetrics 14, 583–592 (2003)
Simpson, D., Lindgren, F., Rue, H.: Fast approximate inference with INLA: the past, the present and the future. arXiv:1105.2982v1 [stat.CO]
Acknowledgements
The authors acknowledge Professor José Borges for providing access to data collected by the Remote Sensing Laboratory of Instituto Superior de Agronomia, Professor M. Antónia Amaral-Turkman for sharing the WinBugs code of the model in paper [1] and to the anonymous referee for very useful and pertinent comments on a previous paper version. Research partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal—FCT, under the projects PEst-OE/SAU/UI0447/2011 and PEst-OE/MAT/UI0006/2011.
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Natário, I., Oliveira, M.M., Marques, S. (2014). Using INLA to Estimate a Highly Dimensional Spatial Model for Forest Fires in Portugal. In: Pacheco, A., Santos, R., Oliveira, M., Paulino, C. (eds) New Advances in Statistical Modeling and Applications. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-05323-3_23
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