  This talk will review a little over a decade's research on applying certain
stochastic models to biological sequence analysis. The models themselves have a
longer history, going back over 30 years, although many novel variants have
arisen since that time. The function of the models in biological sequence
analysis is to summarize the information concerning what is known as a motif or
a domain in bioinformatics, and to provide a tool for discovering instances of
that motif or domain in a separate sequence segment. We will introduce the
motif models in stages, beginning from very simple, non-stochastic versions,
progressively becoming more complex, until we reach modern profile HMMs for
motifs. A second example will come from gene finding using sequence data from
one or two species, where generalized HMMs or generalized pair HMMs have proved
to be very effective.
