# Quantification of annual wildfire risk; A spatio-temporal point process approach.

## DOI:

https://doi.org/10.6092/issn.1973-2201/3985## Abstract

Policy responses for local and global firemanagement depend heavily on the proper understanding of the fire extent as well as its spatio-temporal variation across any given study area. Annual fire risk maps are important tools for such policy responses, supporting strategic decisions such as location-allocation of equipment and human resources. Here, we define risk of fire in the narrow sense as the probability of its occurrence without addressing the loss component. In this paper, we study the spatio-temporal point patterns of wildfires and model them by a log Gaussian Cox processes. Themean of predictive distribution of randomintensity function is used in the narrow sense, as the annual fire risk map for next year.

## References

M. A. AMARAL TURKMAN, K. F. TURKMAN, L. P. YANNICK, J. M. C. PEREIRA (2011). Hierarchical space-time models for fire ignition and percentage of land burned by wildfires. Environmental and Ecological Statistics, 18, pp. 601–617.

A. BADDELEY, J. MØLLER, A. G. PAKES (2008). Properties of residuals for spatial point processes. Annals of the Institute of Statistical Mathematics, 60, pp. 627–649.

F. BONNEU (2007). Exploring and modeling fire department emergencies with a spatiotemporal marked point process. Case Studies in Business, Industry and Government Statistics, 1, no. 2, pp. 139–152.

A. BRIX, P. J. DIGGLE (2001). Spatiotemporal prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63, no. 4, pp. 823–841.

C. CZADO, T. GNEITING, L. HELD (2009). Predictive model assessment for count Data. Biometrics, 65, no. 4, pp. 1254–1261.

P. DE ZEA BERMUDEZ, J. MENDES, J. M. C. PEREIRA, K. F. TURKMAN, M. J. P. VASCONCELOS (2009). Spatial and temporal extremes ofwildfire sizes in Portugal (1984-2004). Internacional Journal ofWildland Fire, 18, no. 8, pp. 983–991.

P. J. DIGGLE (2003). Statistical analysis of spatial point patterns. Arnold, second ed.

T. GNEITING (2002). Nonseparable, stationary covariance functions for space-time data. Journal of the American Statistical Association, 97, pp. 590–600.

T. GNEITING, F. BALABDAOUI, A. E. RAFTERY (2007). Probabilistic forecasts, calibration and sharpness. Journal of the Royal Statistical Society, Series B, 69, no. 2, pp. 243–268.

M. M. HOSSAIN, A. B. LAWSON (2009). Approximate methods in Bayesian point process spatial models. Computational Statistics and Data Analysis, 53, no. 8, pp. 2831–2842.

J. B. ILLIAN, S. H. SØRBYE, H. RUE (2012). A toolbox for fitting complex spatial point processmodels using integrated nested Laplace approximation (INLA). Annals ofApplied Statistics, 6, no. 4, pp. 1499–1530.

J. B. ILLIAN, S. H. SØRBYE, H. RUE, D. K. HENDRICHSEN (2010). Fitting a log GaussianCox processwith temporally varying effects - a case study. Tech.Rep. 17, Department of Mathematical Sciences, Norwegian University of Science and Techonology.

S. LIANG, B. P.CARLIN, A. E.GELFAND (2009). Analysis ofMinnesota colon and rectum cancer point patterns with spatial and non-spatial covariate information. Annals of Applied Statistics, 3, no. 3, pp. 943–962.

F. LINDGREN, H. RUE, J. LINDSTRÖM (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (with discussion). Journal of the Royal Statistical Society, Series B, 73, no. 4, pp. 423–498.

J. M.MENDES, P. DE ZEA BERMUDEZ, J.M. C. PEREIRA, K. F. TURKMAN, ,M. J. P. VASCONCELOS (2010). Spatial extremes of wildfire sizes: Bayesian hierarchical models for extremes. Environmental and Ecological Statistics, 17, pp. 1–28.

J. MØLLER, C. DIAZ-AVALOS (2010). Structured spatio-temporal shot-noise Cox point process models, with a view to modelling forest fires. Scandinavian Journal of Statistics, 37, pp. 2–15.

J. MØLLER, A. R. SYVERSVEEN, R. P. WAAGEPETERSEN (1998). Log Gaussian Cox processes. Scandinavian Journal of Statistics, 25, pp. 451–482.

E. A. REIS (2008). Modelos dinâmicos Bayesianos para processos pontuais espaço-temporais. Ph.D. thesis, Universidade Federal do Rio de Janeiro.

E. A. REIS, D. GAMERMAN, M. S. PAEZ, T. G. MARTINS (2013). Bayesian dynamic models for space-time point processes. Computational Statistics and Data Analysis, 60, pp. 146–156.

H. RUE, S. MARTINO, N. CHOPIN (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B, 71, no. 2, pp. 319–392.

F. P. SCHOENBERG (2004). Testing separability in spatial-temporal marked point processes. Biometrics, 60, pp. 471–481.

D. SIMPSON, J. ILLIAN, F. LINDGREN, S. H. SØRBYE, H. RUE (2011). Going off grid: Computationally efficient inference for log-Gaussian Cox processes. Tech. Rep. 10, Department of Mathematical Sciences, Norwegian University of Science and Techonology.

K. F. TURKMAN, M. A. AMARAL TURKMAN, J. M. C. PEREIRA (2010). Asymptotic models and inference for extremes of spatio-temporal data. Extremes, 13, pp. 375–397.

K. F. TURKMAN, M. A. AMARAL TURKMAN, P. PEREIRA, A. SÁ, J. M. C. PEREIRA (2013). Generating annual fire risk maps using Bayesian hierarchical models. Journal of Statistical Theory and Practice. Under review.

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*Statistica*,

*73*(1), 55–68. https://doi.org/10.6092/issn.1973-2201/3985

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