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## 02433 Hidden Markov models

In collaboration with Lund University

### Danish title:

Skjulte Markov modeller

5

### Course type:

 Advanced course Taught under open university

Spring

### Scope and form:

Web-based course relying on self-study by the student.

13 weeks

### Date of examination:

Decide with teacher

### Participants restrictions:

Minimum  1, Maximum:  30

### General course objectives:

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.

### Learning objectives:

A student who has met the objectives of the course will be able to:
• 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.

### Content:

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.

### Course literature:

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

### Remarks:

International course.

### Responsible:

Gilles Guillot, 305, 118, (+45) 4525 3321,

### Department:

02 Department of Informatics and Mathematical Modeling

Lund University

At CampusNet

### Keywords:

Time series, state-space models, dynamical systems
Last updated: May 23, 2012

See course in DTU Course base

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