{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T17:41:41Z","timestamp":1778175701053,"version":"3.51.4"},"reference-count":66,"publisher":"Emerald","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,12,23]]},"abstract":"<jats:p>Markov switching models (MSMs) are probabilistic models that employ multiple sets of parameters to describe different dynamic regimes that a time series may exhibit at different periods of time. The switching mechanism between regimes is controlled by unobserved random variables that form a first-order Markov chain. Explicit-duration MSMs contain additional variables that explicitly model the distribution of time spent in each regime. This allows to define duration distributions of any form, but also to impose complex dependence between the observations and to reset the dynamics to initial conditions. Models that focus on the first two properties are most commonly known as hidden semi-Markov models or segment models, whilst models that focus on the third property are most commonly known as changepoint models or reset models. In this monograph, we provide a description of explicitduration modelling by categorizing the different approaches into three groups, which differ in encoding in the explicit-duration variables different information about regime change\/reset boundaries. The approaches are described using the formalism of graphical models, which allows to graphically represent and assess statistical dependence and therefore to easily describe the structure of complex models and derive inference routines. The presentation is intended to be pedagogical, focusing on providing a characterization of the three groups in terms of model structure constraints and inference properties. The monograph is supplemented with a software package that contains most of the models and examples described1. The material presented should be useful to both researchers wishing to learn about these models and researchers wishing to develop them further.<\/jats:p>","DOI":"10.1561\/2200000054","type":"journal-article","created":{"date-parts":[[2014,12,23]],"date-time":"2014-12-23T09:11:37Z","timestamp":1419325897000},"page":"803-886","source":"Crossref","is-referenced-by-count":12,"title":["Explicit-Duration Markov Switching Models"],"prefix":"10.1108","volume":"7","author":[{"given":"Silvia","family":"Chiappa","sequence":"first","affiliation":[{"name":"Statistical Laboratory, University of Cambridge, Microsoft Research Cambridge ,","place":["UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2014,12,23]]},"reference":[{"key":"2026033014112687400_ref001","volume-title":"Bayesian online changepoint detection","author":"Adams","year":"2007"},{"key":"2026033014112687400_ref002","first-page":"17:439","article-title":"Nonlinear Bayesian estimation using Gaussian sum approximations","volume-title":"IEEE Transactions on Automatic Control","author":"Alspach","year":"1972"},{"key":"2026033014112687400_ref003","first-page":"7:2515","article-title":"Expectation correction for smoothing in switching linear Gaussian state space models","volume-title":"Journal of Machine Learning Research","author":"Barber","year":"2006"},{"key":"2026033014112687400_ref004","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804779","volume-title":"Bayesian Reasoning and Machine Learning","author":"Barber","year":"2012"},{"issue":"6","key":"2026033014112687400_ref005","first-page":"18","article-title":"Graphical models for time-series","volume":"27","author":"Barber","year":"2010","journal-title":"IEEE Signal Processing Magazine"},{"key":"2026033014112687400_ref006","volume-title":"Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA Analysis","author":"Barbu","year":"2008"},{"key":"2026033014112687400_ref007","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop","year":"2006"},{"key":"2026033014112687400_ref008","volume-title":"Inference in Bayesian time-series models","author":"Bracegirdle","year":"2013"},{"key":"2026033014112687400_ref009","first-page":"190","article-title":"Switch-reset models: Exact and approximate inference","volume":"15","author":"Bracegirdle","year":"2011","journal-title":"Proceedings of The Fourteenth International Conference on Artificial Intelligence and Statistics"},{"issue":"4","key":"2026033014112687400_ref010","doi-asserted-by":"crossref","first-page":"2191","DOI":"10.1016\/j.csda.2006.07.021","article-title":"Stylized facts of financial time series and hidden semi-Markov models","volume":"51","author":"Bulla","year":"2006","journal-title":"Computational Statistics and Data Analysis"},{"issue":"2","key":"2026033014112687400_ref011","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1109\/TSA.2005.852985","article-title":"A generative model for music transcription","volume":"14","author":"Cemgil","year":"2006","journal-title":"IEEE Transactions on Audio, Speech Lang. Processing"},{"issue":"12","key":"2026033014112687400_ref012","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1109\/TIP.1995.8875996","article-title":"Variable duration hidden Markov model and morphological segmentation for handwritten word recognition","volume":"4","author":"Chen","year":"1995","journal-title":"IEEE Transactions on Image Processing"},{"key":"2026033014112687400_ref013","volume-title":"Analysis and Classification of EEG Signals using Probabilistic Models for Brain Computer Interfaces","author":"Chiappa","year":"2006"},{"key":"2026033014112687400_ref014","first-page":"3","article-title":"A Bayesian approach to switching linear Gaussian state-space models for unsupervised time-series segmentation","volume-title":"Proceedings of Seventh International Conference on Machine Learning and Applications","author":"Chiappa","year":"2008"},{"key":"2026033014112687400_ref015","first-page":"388","article-title":"Movement extraction by detecting dynamics switches and repetitions","volume-title":"Advances in Neural Information Processing Systems 23","author":"Chiappa","year":"2010"},{"issue":"1","key":"2026033014112687400_ref016","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":"Journal of the Royal Statistical Society. Series B"},{"issue":"4","key":"2026033014112687400_ref017","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/LSP.2012.2184795","article-title":"Inference in hidden Markov models with explicit state duration distributions","volume":"19","author":"Dewar","year":"2012","journal-title":"IEEE Signal Processing Letters"},{"issue":"5","key":"2026033014112687400_ref018","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1109\/78.995067","article-title":"An MCMC sampling approach to estimation of nonstationary hidden Markov models","volume":"50","author":"Djuri\u0107","year":"2002","journal-title":"IEEE Transactions on Signal Processing"},{"key":"2026033014112687400_ref019","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511790492","volume-title":"Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids","author":"Durbin","year":"1998"},{"key":"2026033014112687400_ref020","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1017\/CBO9780511984679.011","volume-title":"Bayesian Time Series Models","author":"Eckley","year":"2011"},{"key":"2026033014112687400_ref021","doi-asserted-by":"crossref","first-page":"I\u2013880","DOI":"10.1109\/ICIP.2002.1038166","article-title":"Hidden semi-Markov event sequence models: Application to brain functional MRI sequence analysis","volume":"1","author":"Faisan","year":"2002","journal-title":"International Conference on Image Processing"},{"issue":"2","key":"2026033014112687400_ref022","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s11222-006-8450-8","article-title":"Exact and efficient Bayesian inference for multiple changepoint problems","volume":"16","author":"Fearnhead","year":"2006","journal-title":"Statistics and Computing"},{"issue":"4","key":"2026033014112687400_ref023","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1111\/j.1467-9868.2007.00601.x","article-title":"Online inference for multiple changepoint problems","volume":"69","author":"Fearnhead","year":"2007","journal-title":"Journal of the Royal Statistical Society Series B"},{"issue":"485","key":"2026033014112687400_ref024","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1198\/jasa.2009.0009","article-title":"Bayesian analysis of isochores","volume":"104","author":"Fearnhead","year":"2009","journal-title":"Journal of the American Statistical Association"},{"key":"2026033014112687400_ref025","first-page":"143","article-title":"Variable duration models for speech","volume-title":"Symposium on the Application of Hidden Markov Models to Text and Speech","author":"Ferguson","year":"1980"},{"key":"2026033014112687400_ref026","volume-title":"The theory of segmental hidden Markov models","author":"Gales","year":"1993"},{"key":"2026033014112687400_ref027","volume-title":"Kalman Filtering: Theory and Practice","author":"Grewal","year":"1993"},{"issue":"8","key":"2026033014112687400_ref028","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1109\/78.91145","article-title":"Isolated-utterance speech recognition using hidden Markov models with bounded state durations","volume":"39","author":"Gu","year":"1991","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"4","key":"2026033014112687400_ref029","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1006\/jtbi.2001.2392","article-title":"Pattern analysis in branching and axillary flowering sequences","volume":"212","author":"Gu\u00e9don","year":"2001","journal-title":"Journal of Theoretical Biology"},{"issue":"2","key":"2026033014112687400_ref030","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2307\/1912559","article-title":"A new approach to the economic analysis of nonstationary time series and the business cycle","volume":"57","author":"Hamilton","year":"1989","journal-title":"Econometrica"},{"issue":"1-2","key":"2026033014112687400_ref031","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0304-4076(90)90093-9","article-title":"Analysis of time series subject to changes in regime","volume":"45","author":"Hamilton","year":"1990","journal-title":"Journal of Econometrics"},{"key":"2026033014112687400_ref032","first-page":"11:231","article-title":"Estimation, inference, and forecasting of time series subject to changes in regime","volume-title":"Handbook of Statistics","author":"Hamilton","year":"1993"},{"key":"2026033014112687400_ref033","first-page":"603","article-title":"Variable duration motion texture for human motion modeling","volume-title":"Proceedings of the 9th Pacific Rim International Conference on Artificial Intelligence","author":"Huang","year":"2006"},{"key":"2026033014112687400_ref034","first-page":"434","article-title":"Semi-supervised learning of probabilistic models for ECG segmentation","volume":"1","author":"Hughes","year":"2004","journal-title":"Conference Proceedings of the IEEE Engineering in Medicine and Biology Society"},{"key":"2026033014112687400_ref035","volume-title":"Hidden Markov Model with Binned Duration and Its Application","author":"Jiang","year":"2010"},{"key":"2026033014112687400_ref036","first-page":"7:945","article-title":"Segmental hidden Markov models with random effects for waveform modeling","volume-title":"Journal of Machine Learning Research","author":"Kim","year":"2006"},{"key":"2026033014112687400_ref037","volume-title":"Probabilistic Graphical Models: Principles and Techniques","author":"Koller","year":"2009"},{"key":"2026033014112687400_ref038","first-page":"1241","article-title":"Continuously variable duration hidden Markov models for speech analysis","volume":"11","author":"Levinson","year":"1986","journal-title":"IEEE International Conference on Acoustics, Speech, and Signal Processing"},{"issue":"7","key":"2026033014112687400_ref039","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1016\/j.patrec.2011.02.015","article-title":"An improved noise-robust voice activity detector based on hidden semi-Markov models","volume":"32","author":"Liang","year":"2011","journal-title":"Pattern Recognition Letters"},{"issue":"443","key":"2026033014112687400_ref040","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1080\/01621459.1998.10473764","article-title":"Rejection control and sequential importance sampling","volume":"93","author":"Liu","year":"1998","journal-title":"Journal of the American Statistical Association"},{"key":"2026033014112687400_ref041","doi-asserted-by":"crossref","DOI":"10.1002\/9780470191613","volume-title":"The EM Algorithm and Extensions","author":"McLachlan","year":"2008"},{"issue":"6","key":"2026033014112687400_ref042","doi-asserted-by":"crossref","first-page":"1850","DOI":"10.1109\/TASL.2007.901312","article-title":"Switching linear dynamical systems for noise robust speech recognition","volume":"15","author":"Barber","year":"2007","journal-title":"IEEE Transactions of Audio, Speech and Language Processing"},{"issue":"3","key":"2026033014112687400_ref043","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1109\/89.388149","article-title":"On the complexity of explicit duration HMMs","volume":"3","author":"Mitchell","year":"1995","journal-title":"IEEE Transactions on Speech and Audio Processing"},{"issue":"1","key":"2026033014112687400_ref044","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.dsp.2003.07.003","article-title":"Speech reconstruction using a generalized HSMM (GHSMM)","volume":"14","author":"Moore","year":"2004","journal-title":"Digital Signal Processing"},{"key":"2026033014112687400_ref045","volume-title":"Hidden semi-Markov models (HSMMs)","author":"Murphy","year":"2002"},{"key":"2026033014112687400_ref046","volume-title":"Machine Learning: a Probabilistic Perspective","author":"Murphy","year":"2012"},{"key":"2026033014112687400_ref047","first-page":"77:103","article-title":"Learning and inferring motion patterns using parametric segmental switching linear dynamic systems","volume-title":"International Journal of Computer Vision","author":"Oh","year":"2008"},{"issue":"5","key":"2026033014112687400_ref048","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1109\/89.536930","article-title":"From HMM\u2019s to segment models: a unified view of stochastic modeling for speech recognition","volume":"4","author":"Ostendorf","year":"1996","journal-title":"IEEE Transactions on Speech and Audio Processing"},{"key":"2026033014112687400_ref049","first-page":"981","article-title":"Learning switching linear models of human motion","volume-title":"Advances in Neural Information Processing Systems 13","author":"Pavlovic","year":"2001"},{"key":"2026033014112687400_ref050","volume-title":"Probabilistic Reasoning in Intel ligent Systems: Networks of Plausible Inference","author":"Pearl","year":"1988"},{"issue":"5","key":"2026033014112687400_ref051","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1109\/TSA.2005.858542","article-title":"Classification of musical patterns using variable duration hidden Markov models","volume":"14","author":"Pikrakis","year":"2006","journal-title":"IEEE Transactions on Audio, Speech, and Language Processing"},{"issue":"9","key":"2026033014112687400_ref052","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1109\/TPAMI.2008.191","article-title":"Factorial switching linear dynamical systems applied to physiological condition monitoring","volume":"31","author":"Quinn","year":"2009","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026033014112687400_ref053","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/5.18626","article-title":"A tutorial on hidden Markov models and selected applications in speech recognition","volume":"77","author":"Rabiner","year":"1989","journal-title":"Proceedings of the IEEE"},{"issue":"8","key":"2026033014112687400_ref054","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.2514\/3.3166","article-title":"Maximum likelihood estimates of linear dynamic systems","volume":"3","author":"Rauch","year":"1965","journal-title":"AIAA Journal"},{"key":"2026033014112687400_ref055","first-page":"499","article-title":"A segmental HMM for speech pattern matching","volume-title":"IEEE International Conference on Acoustics, Speech and Signal Processing","author":"Russell","year":"1993"},{"key":"2026033014112687400_ref056","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1109\/ICASSP.1985.1168477","article-title":"Explicit modelling of state occupancy in hidden Markov models for automatic speech recognition","volume":"10","author":"Russell","year":"1985","journal-title":"IEEE International Conference on Acoustics, Speech, and Signal Processing"},{"key":"2026033014112687400_ref057","first-page":"38A:142","article-title":"Fitting hidden semi-Markov models to breakpoint rainfall data","volume-title":"Journal of Applied Probability","author":"Sansom","year":"2001"},{"issue":"3","key":"2026033014112687400_ref058","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1109\/TAC.2008.919531","article-title":"Unscented Rauch-Tung-Striebel smoother","volume":"53","author":"S\u00e4rkk\u00e4","year":"2008","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1\/2","key":"2026033014112687400_ref059","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1089\/10665270050081496","article-title":"Bayesian segmentation of protein secondary structure","volume":"7","author":"Schmidler","year":"2000","journal-title":"Journal of Computational Biology"},{"issue":"2","key":"2026033014112687400_ref060","doi-asserted-by":"crossref","first-page":"ii215","DOI":"10.1093\/bioinformatics\/btg1080","article-title":"Gene prediction with a hidden Markov model and a new intron submodel","volume":"19","author":"Stanke","year":"2003","journal-title":"Bioinformatics"},{"key":"2026033014112687400_ref061","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/978-1-4613-8997-2_8","volume-title":"Autonomous Robot Vehicles","author":"Wang","year":"1990"},{"key":"2026033014112687400_ref062","doi-asserted-by":"crossref","DOI":"10.1155\/2010\/761360","article-title":"Hidden Markov model with duration side information for novel HMMD derivation, with application to eukaryotic gene finding","volume-title":"EURASIP Journal on Advances in Signal Processing","author":"Winters-Hilt","year":"2010"},{"issue":"2","key":"2026033014112687400_ref063","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.artint.2009.11.011","article-title":"Hidden semi-Markov models","volume":"174","author":"Yu","year":"2010","journal-title":"Artificial Intelligence"},{"issue":"1","key":"2026033014112687400_ref064","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/LSP.2002.806705","article-title":"An efficient forward-backward algorithm for an explicit-duration hidden Markov model","volume":"10","author":"Yu","year":"2003","journal-title":"IEEE Signal Processing Letters"},{"issue":"2","key":"2026033014112687400_ref065","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/S0165-1684(02)00378-X","article-title":"A hidden semi-Markov model with missing data and multiple observation sequences for mobility tracking","volume":"83","author":"Yu","year":"2003","journal-title":"Signal Processing"},{"key":"2026033014112687400_ref066","author":"Zoeter","year":"2005","journal-title":"Monitoring Non-Linear and Switching Dynamical Systems"}],"container-title":["Foundations and Trends\u00ae in Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftmal\/article-pdf\/7\/6\/803\/11154007\/2200000054en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftmal\/article-pdf\/7\/6\/803\/11154007\/2200000054en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T18:10:57Z","timestamp":1777486257000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftmal\/article\/7\/6\/803\/1332386\/Explicit-Duration-Markov-Switching-Models"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,23]]},"references-count":66,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2014,12,23]]}},"URL":"https:\/\/doi.org\/10.1561\/2200000054","relation":{},"ISSN":["1935-8237","1935-8245"],"issn-type":[{"value":"1935-8237","type":"print"},{"value":"1935-8245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,23]]}}}