Low-order approximations of Markov chains in a decision theoretic context (Corresp.)
Demetrios Kazakos · IEEE Transactions on Information Theory · 1980
The idea of finding a low-order approximation to a Markov chain is considered. The approximating process is characterized by a smaller number of parameters than the original one. As a criterion for approximation the lower order process is required to be the most difficult to discriminate from the original one in a decision theoretical context, i.e., achieving maximal Bayes error probability. It is shown that the Hellinger distance metric is closely related to the discrimination performance and provides robust approximation. It is then used to derive the best memoryless approximation, with a possibly reduced number of states, to a first-order Markov chain.