Keywords
search area
continuous surfaces
mean random distance
mapping of areas
How to Cite
##article.highlights##
- A total of 13 bandwidth values (h) were defined using seven techniques.
- Great variation was observed in the values obtained from h (between 2 550 and 41 906 m).
- The statistically most adequate h value was defined between 5 300 and 5 900 m.
- The h value closest to the optimum range was obtained by means of the mean random distance technique (5 395 m).
- It is possible to select h under statistical criteria avoiding the use of subjective criteria.
Abstract
Introduction. The mapping of areas with higher forest fire density can be developed through kernel density estimation, which requires the selection of a function and bandwidth (h). The h value, when defined by subjective (visual) processes, will depend on the knowledge and experience of the person making the selection.
Objective: To propose a statistical alternative, based on forest fires information (2005-2013) from Jalisco, Mexico, for the selection of h as support for kernel density estimation.
Materials and methods: A total of 13 h values were defined using seven techniques. The h value was selected using the following statistics: root mean square error, root mean integrated squared error, coefficient of variation and comparative percentage.
Results and discussion: The h values obtained with the techniques analyzed were between 2 550 and 41 906 m. There was great variation in the results; the range between the maximum and the minimum value was 39 356.34 m with an average of 10 936.74 ± 9 955.04 m. The above implies that there is no single and universal process for all cases. According to the validation criteria, the statistically most adequate h value is between 5 300 and 5 900 m; the closest result was obtained with the mean random distance technique (5 395 m).
Conclusion: It is possible to select h under a practical statistical perspective, avoiding the use of subjective criteria.
References
Álvarez, E., & Yohai, V. (2012). M-estimators for isotonic regression. Journal of Statistical Planning and Inference, 142(8), 2351–2368. doi: https://doi.org/10.1016/j.jspi.2012.02.051
Amatulli, G., Perez-Cabello, F., & de la Riva, J. (2007). Mapping lighting/human caused wildfires occurrence under ignition point location uncertainty. Ecological Modelling, 200(3-4), 321–333. doi: https://doi.org/10.1016/j.ecolmodel.2006.08.001
Anselin, L., Bera, A. K., Florax, R., & Yoon, M. J. (1996). Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics, 26(1), 77–104. doi: https://doi.org/10.1016/0166-0462(95)02111-6
Comisión Nacional Forestal (CONAFOR). (2015). Incendios. Retrieved August 4, 2015 from http://www.conafor.gob.mx/web/temas-forestales/incendios/
de la Riva, J., Pérez, C. F., Lana, R. N., & Koutsias, N. (2004). Mapping wildfire occurrence at regional scale. Remote Sensing of Environment, 92(3), 363–369. doi: https://doi.org/10.1016/j.rse.2004.06.022.
de Smith, M. J., Goodchild, M. F., & Longley, P. A. (2009). Geospatial analysis. A comprehensive guide to principles, Techniques and software tools (3rd ed.). Winchelsea, UK: The Winchelsea Press. Retrieved from http://www.spatial analysisonline.com/
Fuenzalida, M., Cobs, V., & Guerrero, R. (2013). El territorio como unidad de análisis en estudios sobre las determinantes sociales de la salud. Argos, 30(59), 87–106. Retrieved from http://www.academia.edu/27985206/El_territorio_como_unidad_de_an %C3%A1lisis_en_estudios_sobre_las_determinantes_sociales_de_la_salud
Koutsias, N., Kalabokidis, K., & Allgöwer, B. (2004). Fire occurrence patterns at landscape level: Beyond positional accuracy of ignition points with kernel density estimation methods. Natural Resource Modeling, 17(4), 359–375. doi: https://doi.org/10.1111/j.1939-7445.2004.tb00141.x
Krisp, J. M., Peters, S., Murphy, C. E., & Fan, H. (2009). Visual bandwidth selection for kernel density maps. PFG–Journal of Photogrammetry, Remote Sensing and Geoinformation Science, 5, 445–454. doi: https://doi.org/10.1127/1432-8364/2009/0032
Kulldorff, M., & Nagarwalla, N. (1995). Spatial disease clusters: Detection and inference. Statistics in Medicine, 14(8), 799–810. doi: https://doi.org/10.1002/sim. 4780140809
Kuter, S., Usul, N., & Kuter, N. (2011). Bandwidth determination for kernel density analysis of wildfire events at forest sub-district scale. Ecological Modelling, 222(17), 3033–3040. doi: https://doi.org/10.1016/j.ecolmodel.2011.06.006
Mohammadi, F., Bavaghar, M. R., & Shabanian, N. (2014). Forest fire risk zone modeling using logistic regression and GIS: an Iranian case study. Small-scale Forestry, 13(1), 117–125. doi: https://doi.org/10.1007/s11842-013-9244-4
Salvati, L., & Ferrara, A. (2015). Validation of MEDALUS fire risk index using forest fire statistics through a multivariate approach. Ecological Indicators, 48, 365–369. doi: https://doi.org/10.1016/j.ecolind.2014.08.027
Seaman, D. E., & Powell, R. A. (1996). An evaluation of the accuracy of kernel density estimators for home range analysis. Ecology, 77(7), 2075–2085. Retrieved from http://links.jstor.org/sici?sici=0012-9658%28199610%2977%3A7%3C2075%3AAEOTAO%3E2.0.CO%3B2-%23
Silverman, B. W. (1986). Density estimation for statistics and data analysis. London, UK: Chapman & Hall/CRC. Retrieved fromhttps://ned.ipac.caltech.edu/ level5/March02/Silverman/paper.pdf
Thompson, M. P., Calkin, D. E., Finney, M. A., Gebert, K. M., & Hand, M. S. (2013). A risk-based approach to wildland fire budgetary planning. Forest Science, 59(1), 63–77. doi: https://doi.org/10.5849/forsci.09-124.
Turlach, B. A. (1999). Bandwidth selection in kernel density estimation: A review. Belgium: Institut de Statistique Université Catholique de Louvain. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.44.6770&rep=rep1&type=pdf
Vilar, H. L., Martín, I. M. P., & Martínez, V. F. J. (2011). Logistic regression models for human-caused wildfire risk estimation: analysing the effect of the spatial accuracy in fire occurrence data. European Journal of Forest Research, 130(6), 983–996. doi: https://doi.org/10.1007/s10342-011-0488-2
Vrahimis, A. (2010). Smoothing methodology with applications to nonparametric statistics. Tesis Doctoral, University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/files/54503714/FULL_TEXT
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright (c) 2018 Revista Chapingo Serie Ciencias Forestales y del Ambiente