Approximate Bayesian Classification Based Upon Hidden Markov Modeling

We investigate a Bayesian approach to multiple hpothesis testing for hidden Markov sources, whose statistics are given empirically by training data. The exact Bayesian optimal decision rule involves calculation of conditional means of probability density functions and hence it is computationally untractable. To avoid this difficulty, we propose an alternative decision rule which is computationally more attractive. It is proved that the asymptotic exponential rate of decay of the error probability, associated with the proposed decision rule, is optimal. Furthermore, it does not require knowledge of the prior probability densities of the model parameters. The approach is generalized to hypotheses testing in a noisy environment, given training data of the clean sources and the noise process. Simulation results on computer generated hidden Markov processes reveal significant preference of the proposed approach over a standard method currently used.