Uma medida de contribuição local para sequências de processos fora de regime permanente

• Ano de defesa: 2015
• Autor(a) principal: Silvio Alves de Souza
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Engenharia Elétrica; Engenharia elétrica
• Link de acesso: http://hdl.handle.net/1843/BUBD-9Y7HQN

In this work we let us consider a set with a finite number of sequences, discrete and continuous. The main goal in this work is to measure instantaneously the contribution of each sequence of this set to the marginal probability distribution of another, instantaneously, in the discrete case. In the continuous case, to measure the contribution of each transition density function of these sequences to the marginal transition function of another one instantaneously. In the discrete case let us consider categorical sequences generated by sources with the same alphabet. The contribution found is measured by the weight parameter of a special linear combination involving information of all sequences. The coefficients of this combination are denominated local contribution coefficients and represent how much each marginal probability distribution contributes to calculate of another. Therefore it is possible to know in real time how probable an outcome is based on the outcomes of all other sequences. The methodology proposed here extends the models given in Ching2002 and Ching2008 for Markov chains to Probabilistic Context Tree models. An algorithm to estimate the local contribution of each sequence to marginal distributions as time evolves is presented. Simulation results show that the estimated marginal distribution using the model is close to the true one. The proposed methodology is applied to a Historical Portuguese electronic corpus of texts written in Portuguese by authors born between 1380 and 1845 codified according to rhythmic features. In continuous case a methodology to measure the contribution of one sequence (time series) to another sequence using the marginal probability of the process is proposed. A set of sequences with continuous space state and discrete time with Markovian dependence structure on the past is considered. Such a measure is not a measure of (dis)similarity between time series, but a measure of contribution of one sequence towards another sequence. To this end, the cross marginal transition density function across continuous Markov chains is defined and a model that expresses the marginal transition density function of a determined chain as a linear combination of all the other marginal transition density functions is proposed. This contribution is measured by the weight parameter of a special linear combination involving information of all the other density functions. In this way the marginal transition density takes into account information of all other sequences. The coefficients of this combination are also denominated local contribution coefficients and represent how much each transition density function contributes to the calculation of the determined transition density function. As a result an algorithm to estimate the local contribution of each sequence of density functions is presented. In order to estimate the marginal density functions a kernel-based estimator is used. Simulations, considering 2 chains, are presented so as to check the sensitivity of the proposed model and an example using real data is given.