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Mathematically modelling Bayes’ theorem to investigate the origin of a forest fire

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Spanish

<http://hdl.handle.net/10251/161896>

Abstract

[ES] Mathematic modelling (MMT) is a basic element for teaching mathematics in engineering. The MMT phases would be to translate the actual problem into a mathematical problem, to solve the problem, to interpret the result in real key and finally to validate it. Bayesian probability is one of the topical issues that the future engineer finds in his training. From this approach, the probability is subjective, since it will change to the extent that it is clear that it will be amended. In this communication we will show a project where the Bayesian approach is used, with the help of MATLAB, to establish criteria for finding the origin of a forest fire. The mathematical translation involves identifying the burnt area with an initial matrix which establishes the prima facie probability that each area will be the source of the fire. On the basis of a search method, with a certain degree of effectiveness in detecting the origin of the fire, and with the help of Bayes’ teorema, we will obtain the new probabilities of the origin of the fire after the event. It can be seen that if the investigation in one area turns out to be negative, then the likelihood of that site being the source of the fire decreases and, on the other hand, that of the other uninvestigated areas increases. We will also show the MATLAB scripts that have been used throughout the MMT process and above all in transforming the matrix numbers into a colour map that helps to view the search for the origin of the fire. While the students who carried out the project showed a positive attitude, it should also be stressed that they need greater theoretical foundations to carry it out and to improve the use of MATLAB. The authors would like to thank for the financial support and institutional support received from the University of València through project PIME 19-20/190. ‘Transversal competences in physico-mathematical subjects considered as a control point: development of activities, gathering evidence and assessing without dying in the attempt’ Boigues Plants, FJ; Estruch, V.; Vidal Meló, A. (2021). Mathematically modelling Bayes’ theorem to investigate the origin of a forest fire. EN Proceedings INNODOCT/20. International Conference on Innovation, Documentation and Education. Publishing house Universitat Politècía de València. 313-321. https://doi.org/10.4995/INN2020.2020.11796

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