ST1: Fernando Nascimento
Title: Bayesian inference for the joint distribution of r-largest order statistics with change point
Extreme Value Theory (EVT) can be used in may areas of knowledge as economic and environmental. In some situations, (EVT) analyses only the block maximum of some dataset by the GEV distribution, which can provide few observations, and in those cases, it is more effective to use the joint distribution of the the r largest-order statistics. Environmental and financial time series is subject to abrupt changes in this behaviour. Change point analysis is a statistical tool used to analyze sudden
changes in observations along the time series, where the parameters of the distribution has a change of regime. In this paper, we proposed a change-point model to the joint distribution of the r-largest order statistics. The parameteres of each regime and the change points are estimated under the bayesian paradigm. The number of change points to be used are choosen verifying the behaviour of posterior distribution for different number of change points proposed, and the choice of optimal value of r order statistics to be used is a important aspect analysed. MCMC techniques was used to find the posterior distribution of parameters. Simulations results shows the efficiency of the proposed method of estimation, and application to river quota and stock market showed the advantage to use a r>1 number of order statistics, compared with standard GEV distribution to maxima.
ST2: Leonardo Bastos
Title: Modelling reporting delays for disease surveillance data
One difficulty for real-time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistic problems, infrastructure difficulties, etc. However, some notification systems report not only when the case happen, but also when the information enter in the notification system. Based on this two dates, we developed a hierarchical Bayesian model that update the total reporting cases by estimating the delayed cases. Inference was done under a fast Bayesian approach through an algorithm based on integrated nested Laplace approximation (INLA). We apply the proposed approach in dengue notification data from Rio de Janeiro, Brazil.
ST3: Victor Fossaluza
Title: Coherent Hypothesis Testing
Multiple hypothesis testing, an important quantitative tool to report the results of scientific inquiries, frequently leads to contradictory conclusions. For instance, in an analysis of variance (ANOVA) setting, the same dataset can lead one to reject the equality of two means, say µ1 = µ2, but at the same time to not reject the hypothesis that µ1 = µ2 = 0. These two conclusions violate the coherence principle introduced by Gabriel in 1969, and lead to results that are difficult to communicate, and, many times, embarrassing for practitioners of statistical methods. Although this situation is common in the daily life of statisticians, it is usually not discussed in courses of statistics. In this work, we enrich the teaching and discussion of this important topic by investigating through a few examples whether several standard test procedures are coherent or not. We also discuss the relationship between coherent tests and measures of support. Finally, we show how a Bayesian decision-theoretical framework can be used to build coherent tests. These approaches to coherence enlighten when such property is appealing in multiple testing and provide means of obtaining it.
ST4: Marcos Prates
Title: Spatial Quantile Regression for Wind Speed Prediction
Renewable energy sources have become increasingly important because they are cheap, clean and have smaller impact in the environment. For this reason, wind energy have become an important source of electric power throughout the world. Therefore, to map the wind speed incidence in the state of Minas Gerais is extremely important to determine the location of possible new wind farms and for its strategic planning. Quantile regression allow to perform regression not only in the mean response but different quantiles of interest. This property permit to understand the wind speed behavior over any quantile of interest, this of extreme importance because it allows not only to detect regions with high energy potential but also with long duration of energy generation since a wind farm needs a minimum wind speed to operate properly. To map the wind incidence over different quantiles in the state of Minas Gerais, in this work, we propose a Bayesian spatial quantile hierarchical model that is intuitive and computationally efficient. We end with a real data analysis presenting quantile maps of wind speed and of power potential for the State of Minas Gerais for the summer period of 2016.
Keywords: INLA, Kumaraswamy distribution, Log-Logistic Distribution, Wind speed prediction, Spatial Quantile Regression, SPDE