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

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,[1] part-of-speech tagging, musical score following,[2] partial discharges[3] and bioinformatics.[4][5]