Model structure, properties and methods Preliminaries: mixtures and Markov chains Introduction Independent mixture models Markov chains Exercises Hidden Markov models: definition and properties A simple hidden Markov model The basics The likelihood Exercises Direct maximization of the likelihood Introduction Scaling the likelihood computation Maximization subject to constraints Other problems Example: earthquakes Standard errors and confidence intervals Example: parametric bootstrap Exercises Estimation by the EM algorithm Forward and backward probabilities The EM algorithm Examples of EM applied to Poisson-HMMs Discussion Exercises Forecasting, decoding and state prediction Conditional distributions Forecast distributions Decoding State prediction HMMs for classification Exercises Model selection and checking Model selection by AIC and BIC Model checking with pseudo-residuals Examples Discussion Exercises Bayesian inference for Poisson-HMMs Applying the Gibbs sampler to Poisson-HMMs Bayesian estimation of the number of states Example: earthquakes Discussion Exercises R packages The package depmixS4 The package HiddenMarkov The package msm The package R20penBUGS Discussion Extensions General state-dependent distributions Introduction Univariate state-dependent distribution Multinomial and categorical HMMs Multivariate state-dependent distribution Exercises Covariates and other extra dependencies Introduction HMMs with covariates HMMs based on a second-order Markox chain HMMs with other additional dependencies Exercises Continuous-valued state processes Introduction Models with continous-valued state process Fitting an SSM to the earthquake data Discussion Hidden semi-Markov models as HMMs Introduction Semi-Markov processes, hidden semi-Markov models and approximating HMMs Examples of HSMMs as HMMs General HSMM R code Some examples of dwell-time distributions Fitting HSMMs via the HMM representation Example: earthquakes Discussion Exercises HMMs for longitudinal data Introduction Some parameters constant across components Models with random effects Discussion Exercises Applications Introduction to applications Epileptic seizures Introduction Models fitted Model checking by pseudo-residuals Exercises Daily rainfall occurrence Introduction Models fitted Eruptions of the Old Faithful geyser Introduction The data Binary time series of short and long eruptions Normal-HMMs for durations and waiting times Bivariate model for durations and waiting times Exercises HMMs for animal movement Introduction Directional data HMMs for movement data Basic HMM for Drosophila movement HMMs and HSMMs for bison movement Mixed HMMs for woodpecker movement Exercises Wind direction at Koeberg Introduction Wind direction classified into 16 categories Wind direction as a circular variable Exercises Models for financial series Multivariate HMM for returns on four shares Stochastic volatility models Exercises Births at Edendale Hospital Introduction Models for the proportion Caesarean Models for the total number of deliveries Conclusion Homicides and suicides in Cape Town Introduction Firearm homicides as a proportion of all homicides, suicides and legal intervention homicides The number of firearm homicides Firearm homicide and suicide proportions Proportion in each of the five categories Animal behaviour model with feedback Introduction The model Likelihood evaluation Parameter estimation by maximum likelihood Model checking Inferring the underlying state Models for a heterogeneous group of subjects Other modifications or extensions Application to caterpillar feeding behaviour Discussion Survival rates of Soay sheep Introduction MRR data without use of covariates MRR data involving covariate information Application to Soay sheep data Conclusion 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 Author index Subject index