1 Answers
A hidden Markov model is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it
X
{\displaystyle X}
— with unobservable states. As part of the definition, HMM requires that there be an observable process
Y
{\displaystyle Y}
whose outcomes are "influenced" by the outcomes of
X
{\displaystyle X}
in a known way. Since
X
{\displaystyle X}
cannot be observed directly, the goal is to learn about
X
{\displaystyle X}
by observing
Y
.
{\displaystyle Y.}
HMM has an additional requirement that the outcome of
Y
{\displaystyle Y}
at time
t
=
t
0
{\displaystyle t=t_{0}}
must be "influenced" exclusively by the outcome of
X
{\displaystyle X}
at
t
=
t
0
{\displaystyle t=t_{0}}
and that the outcomes of
X
{\displaystyle X}
and
Y
{\displaystyle Y}
at
t
<
t
0
{\displaystyle t Hidden Markov models are known for their applications to thermodynamics, statistical mechanics, physics, chemistry, economics, finance, signal processing, information theory, pattern recognition - such as speech, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics.