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==Hierarchical Markov models==
Hierarchical Markov models can be applied to categorize human behavior at various levels of abstraction. For example, a series of simple observations, such as a person's ___location in a room, can be interpreted to determine more complex information, such as in what task or activity the person is performing. Two kinds of Hierarchical Markov Models are the [[Hierarchical hidden Markov model]]<ref name="HHMM">{{cite journal |first1=S. |last1=Fine |first2=Y. |last2=Singer |title=The hierarchical hidden markov model: Analysis and applications |journal=Machine Learning |volume=32 |issue=1 |pages=41–62 |year=1998 |doi=10.1023/A:1007469218079|doi-access=free }}</ref> and the Abstract Hidden Markov Model.<ref name="AHMM">{{cite journal |first1=H. H. |last1=Bui |first2=S. |last2=Venkatesh |first3=G. |last3=West |url=https://www.jair.org/index.php/jair/article/view/10316 |title=Policy recognition in the abstract hidden markov model |journal=Journal of Artificial Intelligence Research |volume=17 |pages=451–499 |year=2002 |doi=10.1613/jair.839|doi-access=free }}</ref> Both have been used for behavior recognition.<ref name="HierarchicalLearningAndPlanningInPOMDPs">{{cite thesis |first=G. |last=Theocharous |url=http://dl.acm.org/citation.cfm?id=936140 |title=Hierarchical Learning and Planning in Partially Observable Markov Decision Processes |type=PhD |publisher=Michigan State University |year=2002}}</ref> and certain conditional independence properties between different levels of abstraction in the model allow for faster learning and inference.<ref name="AHMM" /><ref name="RecognitionOfHumanActivityThroughHierarchicalStochasticLearning">{{cite book |first1=S. |last1=Luhr |first2=H. H. |last2=Bui |first3=S. |last3=Venkatesh |first4=G. A. W. |last4=West |chapter-url=http://dl.acm.org/citation.cfm?id=826390 |chapter=Recognition of Human Activity through Hierarchical Stochastic Learning |title=PERCOM '03 Proceedings of the First IEEE International Conference on Pervasive Computing and Communications |pages=416–422 |year=2003 |doi=10.1109/PERCOM.2003.1192766|isbn=978-0-7695-1893-0 |citeseerx=10.1.1.323.928 }}</ref>
==Tolerant Markov model==
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==Markov-chain forecasting models==
Markov-chains have been used as a forecasting methods for several topics, for example price trends<ref name="SLS">{{cite journal |first1=E.G. |last1=de Souza e Silva |first2=L.F.L. |last2=Legey |first3=E.A. |last3=de Souza e Silva |url=https://www.sciencedirect.com/science/article/pii/S0140988310001271 |title=Forecasting oil price trends using wavelets and hidden Markov models |journal=Energy Economics |volume=32 |year=2010}}</ref>, wind power<ref name="CGLT">{{cite journal |first1=A |last1=Carpinone |first2=M |last2=Giorgio |first3=R. |last3=Langella |first4=A. |last4=Testa |title=Markov chain modeling for very-short-term wind power forecasting |journal=Electric Power Systems Research |volume=122 |pages=152–158 |year=2015|doi=10.1016/j.epsr.2014.12.025 |doi-access=free }}</ref> and solar irradiance<ref name="MMW">{{cite journal |first1=J. |last1=Munkhammar |first2=D.W. |last2=van der Meer |first3=J. |last3=Widén |title=Probabilistic forecasting of high-resolution clear-sky index time-series using a Markov-chain mixture distribution model |journal= Solar Energy |volume=184 |pages=688–695 |year=2019|doi=10.1016/j.solener.2019.04.014 }}</ref>. The Markov-chain forecasting models utilize a variety of different settings, from discretizing the time-series<ref name="CGLT" /> to hidden Markov-models combined with wavelets<ref name="SLS" /> and the Markov-chain mixture distribution model (MCM)<ref name="MMW" />.
== See also ==
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