Uma abordagem Bayesiana para a modelagem dos ventos máximos de Sorocaba-SP e Bauru-SP

Abstract

The probabilistic forecast of the occurrence of extreme winds is of great importance for the planning of projects in the agricultural and civil engineering, making possible to avoid or to diminish the destructive impacts. Thus, identifying efficient methodologies for prediction are an urgent matter. In view of these facts, the objective of this work was to compare the Bayesian methodology, evaluating different distributions prior, and maximum likelihood in the prediction of the occurrence of maximum winds, per semester, in Sorocaba-SP and Bauru-SP. It was also evaluated the fitting of the Gumbel distribution and the Generalized Extreme Values (GEV) distribution to the semester data, from January 2006 to December 2016, of the mentioned sites. The normal distribution was used as prior for the elicitation of the information, in the Bayesian methodology, and the prior information was obtained by analyzing the data of maximum speed of Piracicaba-SP. In order to obtain the marginal values of the posterior distributions, the Monte Carlo method was applied via Markov Chain using the software OpenBugs and R. In order to evaluate the best estimation methodology and the best model were verified the Deviance Information Criterion (DIC), the accuracy, precision and mean prediction error of the maximum wind-level estimates for certain return times. The GEV and Gumbel distributions were fitted to the maximum wind speed data series studied. The Gumbel distribution, considering the Bayesian approach with a variance structure prior multiplied by eight, proved to be more efficient in the semi-annual high winds forecast of Sorocaba-SP. For Bauru-SP, the GEV distribution with structure multiplied by eight was the most propitious, presenting more accurate and accurate results. The application of Bayesian inference led to more accurate, accurate and less predictive errors, showing the efficiency of incorporating information prior in the study of maximum wind speed. From these results, predictions of maximum winds were made in Bauru-SP and Sorocaba-SP, for the return times of 2, 5, 10, 25, 50 and 100 semesters, who can help with planning to avoid catastrophes in agriculture , in construction and in the financial sector of the region.