Seleção estatística de árvores de contexto

Abstract

Context trees are models that parsimoniously generalize Markovian models. These models were introduced by Jorma Rissanen in 1983, as an efficient tool in Information Theory. Since then, these models have been widely used in many fields of Probability and Statistics from both theoretical and applied perspectives. Given a sample, a central problem in Statistics is to estimate a model to the observed data. In this work, we are interested in studying some of the main methods discussed in the literature for the statistical selection of context trees. To do this, we will conduct a comparative study between frequentist methods for context tree selection (context algorithm and its variations) and the Bayesian method, using synthetic data obtained via simulations. Additionally, we illustrate the performance of model selection methods through applications in real data related to neuroscience and genetics.