Abstract

Hidden Markov Models (HMMs) can be used to solve a variety of problems from facial recognition and language translation to animal movement characterization and gene discovery. With such problems, we have a sequence of observations that we are not certain is correct—we are not sure our observations accurately reveal the corresponding sequence of actual states, which are hidden—but we do know some important probabilities that will help us. In this chapter, we will develop the probability theory and algorithms for two types of problems that HMMs can solve—calculate the probability that a particular sequence of observations occurs and determine the most likely corresponding sequence of hidden states. The chapter will end with a collection of research projects appropriate for undergraduates.

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