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A '''hidden Markov model''' ('''HMM''') is a [[Markov model]] in which the observations are dependent on a latent (or "hidden") [[Markov process]] (referred to as <math> X </math>). An HMM requires that there be an observable process <math> Y </math> whose outcomes depend on the outcomes of <math>X</math> in a known way. Since <math> X </math> cannot be observed directly, the goal is to learn about state of <math>X</math> by observing <math> Y. </math> By definition of being a Markov model, an HMM has an additional requirement that the outcome of <math> Y </math> at time <math> t = t_0 </math> must be "influenced" exclusively by the outcome of <math> X </math> at <math> t = t_0 </math> and that the outcomes of <math> X </math> and <math> Y </math> at <math> t < t_0 </math> must be conditionally independent of <math> Y </math> at <math> t=t_0 </math> given <math> X </math> at time <math> t = t_0. </math> Estimation of the parameters in an HMM can be performed using [[Maximum likelihood estimation|maximum likelihood]]. For linear chain HMMs, the [[Baum–Welch algorithm]] can be used to estimate the parameters.
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 recognition|speech]],<ref>{{cite web | url=https://scholar.google.com/scholar?q=levinson+hidden+markov+model+tutorial&hl=en&as_sdt=0&as_vis=1&oi=scholart | title=Google Scholar }}</ref> [[handwriting recognition|handwriting]], [[gesture recognition]],<ref>Thad Starner, Alex Pentland. [http://www.cc.gatech.edu/~thad/p/031_10_SL/real-time-asl-recognition-from%20video-using-hmm-ISCV95.pdf Real-Time American Sign Language Visual Recognition From Video Using Hidden Markov Models]. Master's Thesis, MIT, Feb 1995, Program in Media Arts</ref> [[part-of-speech tagging]], musical score following,<ref>B. Pardo and W. Birmingham. [http://www.cs.northwestern.edu/~pardo/publications/pardo-birmingham-aaai-05.pdf Modeling Form for On-line Following of Musical Performances] {{Webarchive|url=https://web.archive.org/web/20120206123155/http://www.cs.northwestern.edu/~pardo/publications/pardo-birmingham-aaai-05.pdf |date=2012-02-06 }}. AAAI-05 Proc., July 2005.</ref> [[partial discharge]]s<ref>Satish L, Gururaj BI (April 2003). "[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=212242 Use of hidden Markov models for partial discharge pattern classification]". ''[[IEEE Transactions on Dielectrics and Electrical Insulation]]''.</ref> and [[bioinformatics]].<ref>{{cite journal|last1=Li|first1=N|last2=Stephens|first2=M|title=Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data.|journal=Genetics|date=December 2003|volume=165|issue=4|pages=2213–33|doi=10.1093/genetics/165.4.2213|pmid=14704198|pmc=1462870}}</ref><ref>{{cite journal |last1=Ernst |first1=Jason |last2=Kellis |first2=Manolis |title=ChromHMM: automating chromatin-state discovery and characterization |journal=Nature Methods |date=March 2012 |volume=9 |issue=3 |pages=215–216 |doi=10.1038/nmeth.1906 |pmid=22373907 |url= |pmc=3577932 }}</ref>
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