TRIPLET PARTIALLY MARKOV CHAINS AND TREES
Wojciech Pieczynski · 2004
Hidden Markov models (HMM), like chains or trees considered in this paper, are widely used in different situations. Such models, in which the hidden process X is a Markov one, allow one estimating the latter from an observed process Y , which can be seen as a noisy version of X . This is possible once the distribution of X conditional on Y is a Markov distribution. These models have been recently generalized to Pairwise Markov models (PMM), in which one assumes the markovianity of ) , ( Y X , and Triplet Markov models (TMM), in which the distribution of ) , ( Y X is the marginal distribution of an Markov model ) , , ( Y U X . In this paper we propose further generalization of TMM by considering that ) , , ( Y U X is a Markov model with respect to ) , ( U X , but is not necessarily a Markov one with respect to Y . We show that in such models, called "partially Markov", classical restoration algorithms remain valid.