Resolução de conflitos de informação utilizando a distribuição floor

Abstract

From the Bayesian point of view, two sources of information are used to study a phenomenon of interest: the prior distribution and the likelihood. Based on these two sources of information, it is possible to use Bayes’ theorem to obtain the posterior distribution, and, from it, make inferences about a phenomenon of interest. The models represent only a picture of reality, and so it is inevitable the occurrence of errors. The misspecification of a model can happen in several ways; among them is the presence of outliers in the sample. When the data being studied are disturbed by outliers, the prior distribution may conflict with the data distribution, thus creating a conflict of information. In this work, we are interested in the problem of conflicting information when there is presence of outliers. In the literature, it was seen that conflict of information are usually resolved by making use of densities with heavy tails. To study heavytailed distributions, the concepts of regular and O-regular variation were used. In this study, we saw that these classes of heavy-tailed distributions can contribute to obtain a robust modeling. The main objective of this paper is to discuss the use of heavy-tailed distributions in problems of conflicting information using the theory of regular and O-regular variation, specifically with the use of the floor distribution. A simulation study at the end of this study showed that the floor distribution is robust to outliers, when comparing it to the exponential distribution.