Likelihood Based Statistical Inference in Hidden Markov Models
Tero A. Aittokallio, Virpi Ahola, Esa Uusipaikka · 1999
The hidden Markov model (HMM) is one type of stochastic signal model which is widely used in modeling and classification 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 condence intervals for model parameters and further for the probability of a new case to be classified, and how these intervals can be used to provide some useful insights into the HMM. First the confidence intervals for the values of the model parameters tell the sufficency of the sample data in the modeling problem. In addition, the confidence intervals for the probabilities of a new case tell the uncertainty of the classification based on the pure probability in classification problem. We show in detail how to compute two different confidence intervals, namely the Wald's and the profile likelihood intervals. We also demonstrate and compare the results of the two approaches in a real example of classification of nasal flow 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.