The Moments of Matched and Mismatched Hidden
Roy L. Streit · 1990
An algorithm for computing the moments of matched and mismatched hidden Markov models from their defining parameters is presented. The algorithm is of general interest because it is an exten- sion of the usual forward-hackward linear recursion. The algorithm computes the joint moments of the posterior likelihood functions (i.e., the scores) by a multilinear recursion involving the joint moments of the random variables associated with the hidden states of the Markov chain. Examples comparing the first two theoretical moments to sim- ulation results are presented. They are of independent interest because they indicate that the distribution of the posterior likelihood function scores for matched and mismatched models are asymptotically log-nor- mal in important special cases and, therefore, are characterized asymptotically by the first two moments alone. One example discusses the effect of a noisy discrete communication channel on a suboptimal classification method based on the distributions of scores rather than on maximum likelihood classification.