Algoritmos de estimação para modelos Markovianos não-homogêneos

Abstract

Hidden Markov models are a statistical paradigm which can be used to mode stochastic processeswhere the observable values are directly dependent on a sequence of hidden random variables.In the context of the hidden Markov model, the system being modeled is considered a Markovprocess with non-observable hidden states, and for each hidden state we have the emission of anobservable value. Hidden Markov models can be homogeneous or non-homogeneous.In this investigation, we present estimation procedures used with Markov models. Parametersestimation is done under Bayesian and frequentist perspectives, comparing the performance ofthese methods using metrics such as mean squared error and bias. Model selection is carried outusing different criteria such as the Bayes Information Criterion and the Deviance InformationCriterion. The smallest mean squared errors and biases were obtained using the Bayesianestimation algorithm. In the frequentist perspective, the Stochastic EM algorithm obtainedresults which were similar to the Bayesian algorithm. The EM algorithm presented problems inthe estimation procedure in all situations studied