Monographs on HMMs

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• Cappé, Moulines, Ryden (2005), Inference in Hidden Markov Models (book targeted primarily at mathematical statisticians – provides comprehensive theoretical background)

• Frühwirth-Schnatter (2006), Finite Mixture and Markov Switching Models (mathematically rigorous yet relatively accessible introduction to mixture models in general, including HMMs)

• Bartolucci, Farcomeni, Pennoni (2012), Latent Markov Models for Longitudinal Data (accessible introductory book, with strong focus on the EM algorithm and on longitudinal data, i.e. multiple time series)

• Murphy (2012), Machine Learning – A Probabilistic Perspective (Chapter 17 gives a very useful overview of key HMM concepts, nonstandard model formulations and associated methods)

• Zucchini, MacDonald, Langrock (2016), Hidden Markov Models for Time Series: An Introduction Using R (book targeted at applied statisticans and users – gives an overview of methods, implementation and applications)

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Seminal papers on HMMs

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• Rabiner (1989), A tutorial on hidden markov models and selected applications in speech recognition, Proceedings of the IEEE

• Ghahramani (2001), An introduction to hidden Markov models and Bayesian networks, Journal of Pattern Recognition and Artificial Intelligence

• Ephraim, Merhav (2002), Hidden Markov processes, IEEE Transactions on Information Theory

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Some relevant methodological papers

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• Robert, Rydén, Titterington (2000), Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method, Journal of the Royal Statistical Society B

• Altman (2007), Mixed hidden Markov models: an extension of the hidden Markov model to the longitudinal data setting, Journal of the American Statistical Association

• Celeux, Durand (2008), Selecting hidden Markov model state number with cross-validated likelihood, Computational Statistics

• Maruotti, Rydén (2009), A semiparametric approach to hidden Markov models under longitudinal observations, Statistics and Computing

• Maruotti (2011), Mixed hidden Markov models for longitudinal data: an overview, International Statistical Review

• Langrock, Kneib, Sohn, DeRuiter (2015), Nonparametric inference in hidden Markov models using P-splines, Biometrics

• Turek, de Valpine, Paciorek (2016), Efficient Markov chain Monte Carlo sampling for hierarchical hidden Markov models, Environmental and Ecological Statistics

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