Hidden Markov Models (HMMs) remains a vibrant area of research in statistics, with many new applications appearing since publication of the first edition.

Walter Zucchini, Iain K. MacDonald, Roland Langrock

Model structure, properties and methods, Preliminaries: mixtures and Markov chains, Hidden Markov models: definition and properties, Direct maximization of the likelihood, Estimation by the EM algorithm, Forecasting, decoding and state prediction, Model selection and checking, Bayesian inference for Poisson-HMMs, R packages, Extensions, Covariates and other extra dependencies, Continuous-valued state processes, Hidden semi-Markov models as HMMs, HMMs for longitudinal data, Applications , Epileptic seizures, Daily rainfall occurrence, Eruptions of the Old Faithful geyser, HMMs for animal movement, Wind direction at Koeberg, Models for financial series, Births at Edendale Hospital, Homicides and suicides in Cape Town, Animal behaviour model with feedback, Survival rates of Soay sheep, Examples of R code, The functions, Examples of code using the above functions, Some proofs Factorization needed for forward probabilities, Two results for backward probabilities, Conditional independence of Xt1 and XTt+1, References