Syllabus academic year 2007/2008

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course might be given in English. FMS091 overlap following cours/es: MAS221, MAS221 och MASM11. Optional for: D4, E4, F4, F4sfm, I4, Pi3, Pi3bm, Pi3bs, Pi3mrk, Pi3sbs. Course coordinator: Anna Lindgren, Director of studies,, Matematisk statistik. Recommended prerequisits: Basic course in Mathematical statistics and at least one additional course, e.g. Stationary stochastic processes or Markov processes. The course might be cancelled if the numer of applicants is less than 16. Assessment: Written and oral project presentation. Further information: The course is also given at the faculty of science with the code MAS221. Home page:

The purpose of the course is to give the students tools and knowledge to, given a data material and a stochastic model description with a problem formulation, be able to identify and formulate relevant quantities, and approximate these quantities numerically using Monte Carlo based methods. The main aim lies in enhancing the scope of statistical problems that the student will be able to solve.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

Simulation based methods of statistical analysis. Markov chain methods for complex problems, e.g. Gibbs sampling and the Metropolis-Hastings algorithm. Bayesian modelling and inference. The re-sampling principle, both non-parametric and parametric. The Jack-knife method of variance estimation. Methods for constructing confidence intervals using re-sampling. Re-sampling in regression. Permutations test as an alternative to both asymptotic parametric tests and to full re-sampling. Examples of mor complicated situations. Effective numerical calculations in re-sampling. The EM-algorithm for estimation in partially observed models.

Sköld, M: Computer Intensive Statistical Methods, Avd. för Matematisk statistik, LU, 2006.