Avaliação de diferentes prioris na estimação dos parâmetros da distribuição GEV e na predição de quantis extremos

Abstract

The Bayesian approach has been widely applied in studies of extreme values ​​due to the possibility of reducing uncertainty in the estimates. However, the way to elicit an informative a priori structure, when dealing with extreme values ​​adjusted through the generalized distribution of extreme values ​​(GEV), is not yet fully established. Thus, the objective of this work was to evaluate different prior structures in a Bayesian approach of the GEV distribution fitted to maximum data from simulation and real data of maximum precipitation. The prior structures used were: Trivariate Normal distributions with variance and covariance matrices multiplied by 1, 4, non-informative Trivariate Normal distribution; Gamma distribution for extreme quantile differences, with different variabilities. For the case with simulated data, the estimation of parameters and quantiles was evaluated with the GEV model associated with each of these prior structures, with respect to the respective real values, through bias and percentage relative mean bias in different simulation scenarios and sample sizes. And for the real data, the objective was to evaluate, through the accuracy and precision of the estimates of the levels of return, the performance of the referred prior structures in a Bayesian approach to the GEV distribution fitted to data of maximum daily precipitations of São João da Boa Vista- SP, from 1971 to 2017. Data of maximum annual rainfall from Lavras-MG and Silvianópolis- MG were used as prior, comparing the deviance information criterion (DIC), accuracy, mean prediction error and interval mean amplitude of the models' maximum precipitation predictions. As for the main results of the simulated case, it was observed that prior structures with less variability produce more accurate estimates of all parameters of the GEV distribution, considering small sample sizes. In the scenarios in which precipitation data were simulated, the model with Gamma prior structure showed lower parameter bias and return levels. For the real data, by the DIC criterion, there were no substantial differences between the models. The model with a trivariate normal prior structure with a matrix of variances and covariances multiplied by 4, with prior information from Silvianópolis, provided more precise and accurate estimates of return levels.