A simple calculation of the joint moments of hidden Markov models

In this paper, an algorithm presented by Streit (1990) to calculate the integer moments of the output sequence probabilities using the probability measures of the hidden Markov models (HMMs) is reformulated in a matrix algebra framework which allows a better understanding of the algorithm. This algorithm arises in the context of the classification of an unknown stochastic process by a set of HMMs using a test statistic which can be approximated by these integer moments. Using this new formulation, a simple way of calculating the joint moments directly from the parameters of the HMMs in a non-iterative way is presented, and an asymptotic analysis of the algorithm is performed