HMMs  Summary
Section 1  Page 1
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Summary
Frequently, patterns do not appear in isolation but as part of a
series in time  this progression can sometimes be used to
assist in their recognition. Assumptions are usually made about
the time based process  a common assumption is that the
process's state is dependent only on the preceding N states 
then we have an order N Markov model. The simplest case is N=1.
Various examples exists where the process states (patterns) are
not directly observable, but are indirectly, and
probabalistically, observable as another set of patterns  we
can then define a hidden Markov model  these models have proved
to be of great value in many current areas of research, notably
speech recognition.
Such models of real processes pose three problems that are
amenable to immediate attack; these are :
 Evaluation : with what probability does a given model
generate a given sequence of observations. The forward
algorithm solves this problem efficiently.
