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Vol: 57(71) No: 3 / September 2012 A Comprehensive Approach of Multinomial Hidden Markov Models Marina Cidota University of Bucharest, Faculty of Mathematics and Computer Science, Department of Computer Science, Str. Academiei No.14, Bucharest, 010014 Romania, e-mail: cidota@fmi.unibuc.ro Monica Dumitrescu University of Bucharest, Faculty of Mathematics and Computer Science, Department of Mathematics, Str. Academiei No.14, Bucharest, 010014 Romania, e-mail: mdumi@fmi.unibuc.ro Keywords: communication channel, hidden Markov model, multinomial response model, nested optimization algorithms Abstract The paper deals with stochastic modeling for communication systems that are influenced by an external ”catalyzer” (e.g. environmental or experimental conditions). For an one dimensional catalyzer, a model named the Logistic HMM (LHMM) was already introduced by the authors. A new extension of Hidden Markov models is now considered, and all three aspects of stochastic modeling are addressed: building the model, its training and model validation. In the current model, the catalyzer can have multiple components and its influence over the system is expressed through multinomial link functions. We introduce a complex training algorithm based on the Baum-Welch scheme, including nested algorithms for optimization such as the Newton - Raphson and the Expectation-Maximization technique for updating the parameters of the model. The validation step is achieved by means of a statistical test of significance that allows us to decide how many and which catalyzers should be included in the Multinomial Hidden Markov model (MHMM). The likelihood ratio test that we apply for model validation is based on the fact that the probability distributions belong to the Exponential class, hence the model verifies the usual regularity conditions and the maximum-likelihood estimates are asymptotically normal. In order to explore the convergence of the proposed training procedure and the validation of the model, a simulation study is provided. References L. E. Baum and J. Eagon, “An inequality with applications to statistical prediction for functions of markov processes and to a model for ecology,” Bull. Amer. Math. Soc., vol. 73, pp. 360 –363, 1967. [2] L. E. Baum, T. Petrie, G. Soules and N. Weiss, “A maximization technique occurring in the statistical analysis of probabilistic functions of markov chains,” Ann. Math. Statistic., vol. 41, pp. 164 – 171, 1970. [3] S. Michalek, H. Lerche, M. Wagner, N. Mitrovic, M. Schiebe, F. Lehmann-Horn and J. 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