Hidden Markov Models

In Section 2.2.2 the idea of a Markov chain was introduced. Markov chains provide

useful models for the analysis of sequence data since we can model the dependence

that is found in biopolymers in a straightforward manner. To do so, we must con-

sider the problem of parameter estimation for Markov chains. After addressing this

problem, we will treat parameter estimation for hidden Markov models, which are

widely used tools for the analysis of sequences of random variables that display

dependence. Throughout this discussion we will suppose that the parameter that in-

dexes the Markov chain is location on a biopolymer, hence we will refer to successive

values as adjacent locations.