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Hidden Markov ProcessesTheory and Applications to Biology$
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M. Vidyasagar

Print publication date: 2014

Print ISBN-13: 9780691133157

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691133157.001.0001

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Hidden Markov Processes: Basic Properties

Hidden Markov Processes: Basic Properties

Chapter:
(p.164) Chapter Six Hidden Markov Processes: Basic Properties
Source:
Hidden Markov Processes
Author(s):

M. Vidyasagar

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691133157.003.0006

This chapter considers the basic properties of hidden Markov processes (HMPs) or hidden Markov models (HMMs), a special type of stochastic process. It begins with a discussion of three distinct types of HMMs and shows that they are all equivalent from the standpoint of their expressive power or modeling ability: Type 1 hidden Markov model, or a HMM of the deterministic function of a Markov chain type; hidden Markov model of Type 2, or a HMM of the random function of a Markov chain type; and hidden Markov model of Type 3, or a HMM of the joint Markov process type. The chapter also examines various issues related to the computation of likelihoods in a HMM before concluding with an overview of the Viterbi algorithm and the Baum–Welch algorithm.

Keywords:   hidden Markov processes, hidden Markov model, Markov chain, likelihood, Viterbi algorithm, Baum–Welch algorithm

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