To give an introduction to the fundamentals of hidden Markov models (HMMs) and enable the student to apply the methodology to time series problems. The methods presented in the course are illustrated with exercises and examples from the real world primarily using R.

• Assess when an HMM approach is relevant given a set of observations and physical knowledge about the system.
• Formulate a hidden Markov model for a dynamical system.
• Estimate the underlying parameters of an HMM.
• Use information criteria to select between alternative models.
• Apply pseudo residuals to evaluate model fit.
• Estimate the most probable sequence of the hidden states.
• Explain the difference between local and global decoding of an HMM.
• Predict future hidden states of an HMM.
• Forecast future observations using HMMs.
• Describe extensions to the basic first order HMM.
• Demonstrate use of HMMs for solving real life problems.

Mixture models. State dependent distributions. Forward probabilities. Backward probabilities. Baum-Welch algorithm (EM algorithm). State estimation. Local decoding. Global decoding. Viterbi algorithm. Model checking. Outlier detection. Pseudo residuals. Second-order Markov chains. Multivariate observations. Parameters with covariates. Models with additional dependencies.

Zucchini, W. and MacDonald, I.L, (2009): Hidden Markov models for Time Series - An introduction using R

International course.