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Introduction
Hidden Markov Models were first described in a series of statistical papers by Leonard E. Baum and other authors in the second half of the 1960s. One of the first applications of HMMs was speech recognition, starting in the mid-1970s. Indeed, one of the most comprehensive explanations on the topic was published in “A Tutorial On Hidden Markov Models And Selected Applications in Speech Recognition”, by Lawrence R. Rabiner in 1989. In the second half of the 1980s, HMMs began to be applied to the analysis of biological sequences, in particular DNA. Since then, they have become ubiquitous in the field of bioinformatics.
Dynamical systems of discrete nature assumed to be governed by a Markov chain emits a sequence of observable outputs. Under the Markov assumption, it is also assumed that the latest output depends only on the current state of the system. Such states are often not known the observer when only the output values are observable.
Example of a hidden Markov