Computer intensive simulation methods,  2008, 10 sp

Lecturer: professor Jukka Corander, Matematiska Institionen, Åbo Akademi

Period 4, 28.3 - 9.5.2008 NB! No lectures on Wednesday April 30th.

NB! The room for the lectures has changed to ASA C 363!

Stochastic simulation based on computer algorithms is currently a persisting reality in a huge number of scientific and commercial settings. Such an approach enables the study of complex systems and models for diverse phenomena, ranging from autonomous navigation of aeroplanes to characterization of atom-level interactions.

The basis of stochastic simulation is anchored in the generation of random numbers with a computer algorithm, such that the generated values follow approximately a specified probabilistic model. A variety of objectives can then be achieved by processing the generated values further, e.g. system optimization and visualization, parameter estimation and many more. A common name for such a simulation-based approach is Monte Carlo methods. Many currently important applications would be impossible to handle in practice without access to Monte Carlo methods. The Monte Carlo approach has important mathematical properties which can be utilized to achieve sufficiently high degree of accuracy

In this course we will study the principles and mathematical properties behind the most central Monte Carlo algorithms and investigate how how they can be utilized in various applications. Distinct from the pre-announcement, there will be no computer practicals, due to the limitation in available time. Instead, there will be 4 weekly hours of lectures and the participants are urged to do computer practicals independently or in groups.

Course material:

The definite source for the statistical theory behind Monte Carlo is: Christian P. Robert and George Casella. Monte Carlo Statistical Methods. 2nd edition, Springer, 2005. However, as many participants may not be willing to buy the book, we will primarily use the excellent lecture material prepared by Petri Koistinen at the Department of Mathematics and statistics, University of Helsinki (available here). The course page by Petri Koistinen provides also an extensive set of useful links to other sources of information related to Monte Carlo. The free e-book by David MacKay contains some material on Monte Carlo methods and their use in information theoretic applications.

Lectures:  Wed 15-17 ASA 363, Fri 13-15 ASA 363 NB! The course starts on Friday 28.3. NB! The lecture room is distinct from the one mentioned in the ÅA study guide, and there will be no supervised computer practicals. However, simulation demonstrations will be considered during the lectures.

Examination: There will be no written examination, but the participants are required to solve the following set of exercises during the Spring term 2008. NB The examination form has changed from the previously announced one.

Exercises: Exercise1, Exercise2, Exercise3, Exercise4, Exercise5, Exercise6, Exercise7, Exercise8, Exercise9

Lecture diary:

Week 13: introduction to Monte Carlo methods

Week 14: repetition of probability calculus, generation of random numbers (Sections 3.1-3.4).

Week 15: fundamental theorem of simulation, mixture models, recursive definitions of multidimensional distributions, graphical model structures

Week 16: independence sampling, sampling-importance resampling, Metropolis-Hastigs sampler.

Week 17: Gibbs sampler, auxiliary variable methods, slice sampler, illustrations.

 Updated by Jukka Corander April 21st 2008.