Inferência em assinaturas de amostras em cadeias de memória de alcance variável

Abstract

The analysis of a stochastic model to describe realistically a practical situation is a hallenge often insurmountable, especially because the real phenomena exhibit dierent dependencies. In this context the Markov models play a fundamental role, since they allow more ecient solutions. A Markov chain fXt; t 2 Zg of order k taking values on an alphabet A nite, has jAjk(jAj .. 1) parameter to be estimated. This number growsexponentially in k, and therefore a more viable alternative in terms of estimation, is the use of variable length memory chains (VLMC), also known in literature as Probabilistic Context Tree (PCT), since in this model we have, in general, to estimate fewer parameters. In this work we introduce the Sample Signature of a Probabilistic Context Tree (PCT) or VLMC, as a way to distinguish samples of discrete random variables coming from dierent sources. The PCT model is much more interesting than Markov chains of xed order because it is more parsimonious in the sense that we need fewer parameters to describe it. Moreover, we introduce the Sample Signature of a PCT and show that it can bring more information about the generating source than the model itself. We face in this work the challenge of prosodic patterns detention in the written texts of the Historical Portuguese Corpus Tycho Brahe by using the Sample Signatures of the texts. We also use the Generalized Estimating Equation marginal model as a tool to obtain the results.