Hidden Markov Model

Hidden Markov Model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a 

Markov process – call it {\displaystyle X} – with unobservable ("hidden") states.

HMM assumes that there is another process {\displaystyle Y} whose behavior "depends" on {\displaystyle X}. The goal is to learn about {\displaystyle X} by observing {\displaystyle Y}. HMM stipulates that, for each time instance {\displaystyle n_{0}}, the conditional probability distribution of {\displaystyle Y_{n_{0}}} given the history {\displaystyle \{X_{n}=x_{n}\}_{n\leq n_{0}}} must not depend on {\displaystyle \{x_{n}\}_{n.

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.