Métodos adaptativos para detecção de Clusters no espaço-tempo

Abstract

New adaptive based methods to the detection and statistical monitoring of changes in the spatial-temporal pattern of a stochastic process are developed in this thesis. Namely, this study focuses on the following methodologies: Adaptive Likelihood Ratio, Adaptive Bayes Factor,and Adaptive Posterior Process. The applications aim to detect emerging space-time clusters, where the collection of possible cluster candidates is excessively large, which could result in a very inecient method. Results are presented, showing that the adaptive approach improves theperformance in two aspects: rst, decreasing the computation to detect emerging clusters at each time, and second, reducing the size of the candidate clustersâ conguration space. Using the adaptive approach, the evaluation of only a relatively small number of candidates is necessary.Additionally, the false alarm rate can be controlled. Real data and simulated data are used to demonstrate the usefulness and the practicality of the methods. Those results conrm the theoretical advantages of the proposed methodologies to detect emerging clusters.