Likelihood Based Statistical Inference in Hidden Markov Models

The hidden Markov model (HMM) is one type of stochastic signal model which is widely used in modeling and classi cation problems. Yet the more advanced statistical inference in this model has been omitted almost in all applications. In this paper we show how to calculate in practise the likelihood based con dence intervals for model parameters and further for the probability of a new case to be classi ed, and how these intervals can be used to provide some useful insights into the HMM. First the con dence intervals for the values of the model parameters tell the su cency of the sample data in the modeling problem. In addition, the con dence intervals for the probabilities of a new case tell the uncertainty of the classi cation based on the pure probability in classi cation problem. We show in detail how to compute two di erent con dence intervals, namely the Wald's and the pro le likelihood intervals. We also demonstrate and compare the results of the two approaches in a real example of classi cation of nasal ow shapes. We found out that this kind of statistical inference of HMMs is very useful and informative, and we recommend that it should be used regulary in the applications of HMMs.